 12.12.2.1: Fill in the blanks. 2x y 3z 03x y 4z 54x 2y 6z 0is called a ______ ...
 12.1: Use a check to determine whether the ordered pair is a solution of ...
 12.12.3.1: Fill in the blanks. If a point lies on the graph of an equation, it...
 12.12.4.1: Fill in the blanks. A ______ is a rectangular array of numbers writ...
 12.12.1.1: Fill in the blanks. ex y 12x y 1 10 is called a ____ of equations.
 12.12.5.1: Fill in the blanks. ` 4 96 1 `is a _____ . The numbers 4 and 1 lie ...
 12.12.2.2: Fill in the blanks. If the first two equations of the system in Exe...
 12.2: Use a check to determine whether the ordered pair is a solution of ...
 12.12.3.2: Fill in the blanks. The process of determining an equation whose gr...
 12.12.4.2: Fill in the blanks. Each number in a matrix is called an _____ or e...
 12.12.1.2: Fill in the blanks. Because the ordered pair (2, 3) satisfies both ...
 12.12.5.2: Fill in the blanks. A determinant is number that is associated with...
 12.12.2.3: Fill in the blanks. Solutions of a system of three equations in thr...
 12.3: See the illustration. a. Give three points that satisfy the equatio...
 12.12.3.3: Write a system of three equations in three variables that models th...
 12.12.4.3: Fill in the blanks. If the order of a matrix is 3 4, it has 3 _____...
 12.12.1.3: Fill in the blanks. When the graphs of the equations of a system ar...
 12.12.5.3: Fill in the blanks. The _____ of in a1 b1 c1a2 b2 c2a3 b3 c3is `a2 ...
 12.12.2.4: Fill in the blanks. The graph of the equation 2x 3y 4z 5 z is a fla...
 12.4: Video Viewing. The graph below by the Diffusion Group (TDG) predict...
 12.12.3.4: Write a system of three equations in three variables that models th...
 12.12.4.4: Fill in the blanks. A matrix that represents the equations of a sys...
 12.12.1.4: Fill in the blanks. In the equation x 3y 1 x, the xterm has an und...
 12.12.5.4: Fill in the blanks. ______ rule uses determinants to solve systems ...
 12.12.2.5: Fill in the blanks. When three planes coincide, the equations of th...
 12.5: Solve each system by the graphing method, if possible. If a system ...
 12.12.3.5: What equation results when the coordinates of the point (2, 3) are ...
 12.12.4.5: Fill in the blanks. Elementary ______ operations can be used on an ...
 12.12.1.5: Refer to the illustration. Determine whether a true or a false stat...
 12.12.5.5: Fill in the blanks. `a bc d `
 12.12.2.6: Fill in the blanks. When three planes intersect in a line, the syst...
 12.6: Solve each system by the graphing method, if possible. If a system ...
 12.12.3.6: The equation y 5x2 6x 1 is written in the form y ax2 bx c. What are...
 12.12.4.6: Fill in the blanks. The matrix 1 0 201 4 d, with 1s down its main _...
 12.12.1.6: Refer to the illustration. a. How many ordered pairs satisfy the eq...
 12.12.5.6: Fill in the blanks. To find the minor of 5, we cross out the elemen...
 12.12.2.7: For each graph of a system of three equations, determine whether th...
 12.7: Solve each system by the graphing method, if possible. If a system ...
 12.12.3.7: Making Statues. An artist makes three types of ceramic statues (lar...
 12.12.4.7: For each matrix, determine the number of rows and the number of col...
 12.12.1.7: If the system e4x 3y 73x 2y 6is to be solved using the elimination ...
 12.12.5.7: Fill in the blanks. In evaluating the determinant below, about what...
 12.12.2.8: Consider the system: 2x y 4z 3x y 2z 1x y 3z 2(1)(2)a. What is the ...
 12.8: Solve each system by the graphing method, if possible. If a system ...
 12.12.3.8: Puppets. A toy company makes a total of 500 puppets in three sizes ...
 12.12.4.8: Fill in the blanks to complete each elementary row operation: a. Ty...
 12.12.1.8: Consider the system: 23x y6 1690.03x 0.02y a. What step should be p...
 12.12.5.8: Fill in the blanks. What is the denominator determinant for the sys...
 12.12.2.9: For the following system, clear the equations of any fractions or d...
 12.9: Solve each system using the substitution method. ex y 42x 3y 7
 12.12.3.9: Nutrition. A dietician is to design a meal using Foods A, B, and C ...
 12.12.4.9: GaussJordan elimination was used to solve a system. The final augm...
 12.12.1.9: Complete each solution. Solve:The solution is ( , 2).y y 3( ) 7y 3x...
 12.12.5.9: Fill in the blanks. What is the denominator determinant for the sys...
 12.12.2.10: What is the purpose of the numbers shown in red in front of the equ...
 12.10: Solve each system using the substitution method. ey 2x 53x 5y 4 e
 12.12.3.10: Nutritional Planning. One ounce of each of three foods has the vita...
 12.12.4.10: a. Which matrix shown below indicates that its corresponding system...
 12.12.1.10: Complete each solution. Solve:The solution is ( , 3).y 2y 2y 7x 2y ...
 12.12.5.10: Fill in the blanks. For the system e3x 2y 14x y 3Dx 7 Dy 5 D and D ...
 12.12.2.11: Use a check to determine whether the ordered triple is a solution o...
 12.11: Solve each system using the elimination (addition) method. ex 2y 11...
 12.12.3.11: Fashion Designer A clothing manufacturer makes coats, shirts, and s...
 12.12.4.11: Explain what each symbolism means. a. R1 4 R2b. 12 R1c. 6R2 R3
 12.12.1.11: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.11: Fill in the blanks. For the system 2x 3y z 8x y z 24x 3y z 6Dx 28 D...
 12.12.2.12: Use a check to determine whether the ordered triple is a solution o...
 12.12: Solve each system using the elimination (addition) method. e4a 5b 9...
 12.12.3.12: Sculpting. A wood sculptor carves three types of statues with a cha...
 12.12.4.12: Complete the solution to solve the system using matrices. e4x y 14x...
 12.12.1.12: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.12: Fill in the blanks. Fill in the blank. If the denominator determina...
 12.12.2.13: Use a check to determine whether the ordered triple is a solution o...
 12.13: Solve each system by any method, if possible. If a system is incons...
 12.12.3.13: NFL Records. Jerry Rice, who played the majority of his career with...
 12.12.4.13: Represent each system using an augmented matrix. See Example 1. ex ...
 12.12.1.13: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.13: Complete the evaluation of each determinant. ` 5 22 6 ` 5( ) (2)(2)...
 12.12.2.14: Use a check to determine whether the ordered triple is a solution o...
 12.14: Solve each system by any method, if possible. If a system is incons...
 12.12.3.14: Hot Dogs. In 10 minutes, the top three finishers in the 2010 Nathan...
 12.12.4.14: Represent each system using an augmented matrix. See Example 1. x y...
 12.12.1.14: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.14: Complete the evaluation of each determinant. 213342153
 12.12.2.15: Solve each system. See Example 2. x y z 42x y z 12x 3y z 1
 12.15: Solve each system by any method, if possible. If a system is incons...
 12.12.3.15: Earths Atmosphere. Use the information in the circle graph to deter...
 12.12.4.15: For each augmented matrix, give the system of equations that it rep...
 12.12.1.15: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.15: Evaluate each determinant. See Example 1. ` ` 2 32 5
 12.12.2.16: Solve each system. See Example 2. x y z 4x y z 2x y 2z 1
 12.16: Solve each system by any method, if possible. If a system is incons...
 12.12.3.16: Deceased Celebrities. Between October 2009 and October 2010, the es...
 12.12.4.16: For each augmented matrix, give the system of equations that it rep...
 12.12.1.16: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.16: Evaluate each determinant. See Example 1. `3 22 4 ` ` 2
 12.12.2.17: Solve each system. See Example 2. 3x 2y 5z 34x 2y 3z 105x 2y 2z 11
 12.17: Solve each system by any method, if possible. If a system is incons...
 12.12.3.17: Triangles. The sum of the measures of the angles of any triangle is...
 12.12.4.17: Perform each of the following elementary row operations on the augu...
 12.12.1.17: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.17: Evaluate each determinant. See Example 1. ` ` 9 74 2 `
 12.12.2.18: Solve each system. See Example 2. 5x 4y 2z 23x 4y 3z 272x 4y 7z 23
 12.18: Solve each system by any method, if possible. If a system is incons...
 12.12.3.18: Quadrilaterals. A quadrilateral is a foursided polygon. The sum of...
 12.12.4.18: Perform each of the following elementary row operations on the augu...
 12.12.1.18: Use a check to determine whether the ordered pair is a solution of ...
 12.12.5.18: Evaluate each determinant. See Example 1. `1 23 4 `
 12.12.2.19: Solve each system. See Example 2. 2x 6y 3z 95x 3y 5z 34x 3y 2z 15
 12.19: Estimate the solution of the system e y 23 x2x 3y 423. from the gra...
 12.12.3.19: TV History. XFiles, Will & Grace, and Seinfeld are three of the mo...
 12.12.4.19: Perform each of the following elementary row operations on the augu...
 12.12.1.19: Solve each system by graphing. See Example 2. ex y 6x y 2
 12.12.5.19: Evaluate each determinant. See Example 1. ` ` 5 2010 6
 12.12.2.20: Solve each system. See Example 2. 4x 3y 5z 232x 5y 3z 134x 6y 7z 7
 12.20: Give one advantage and one disadvantage for each of the following m...
 12.12.3.20: Traffic Lights. At a traffic light, one cycle through greenyellowr...
 12.12.4.20: Perform each of the following elementary row operations on the augu...
 12.12.1.20: Solve each system by graphing. See Example 2. ex y 42x y 5 e
 12.12.5.20: Evaluate each determinant. See Example 1. 10 1515 5
 12.12.2.21: Solve each system. See Example 2. 4x 5y 8z 522x 3y 4z 263x 7y 8z 31
 12.21: Write a system of two equations in two variables to solve each prob...
 12.12.3.21: Ice Skating. Three circles are traced out by a figure skater during...
 12.12.4.21: Perform each of the following elementary row operations on the augm...
 12.12.1.21: Solve each system by graphing. See Example 2. ey 2x 1x 2y 7
 12.12.5.21: Evaluate each determinant. See Example 1. ` ` 6 215 4 `
 12.12.2.22: Solve each system. See Example 2. 2x 6y 3z 205x 3y 5z 474x 3y 2z 4
 12.22: Write a system of two equations in two variables to solve each prob...
 12.12.3.22: NBA Centers. Together, Shaquille ONeil (Boston Celtics) and Dwight ...
 12.12.4.22: Perform each of the following elementary row operations on the augm...
 12.12.1.22: Solve each system by graphing. See Example 2. e 3x y 3y 2x 7 e
 12.12.5.22: Evaluate each determinant. See Example 1. ` 3 212 8 `
 12.12.2.23: Solve each system. See Example 3. 3x 3z 6 4y7x 5z 46 2y4x 31 z
 12.23: Write a system of two equations in two variables to solve each prob...
 12.12.3.23: Potpourri. The owner of a home decorating shop wants to mix dried r...
 12.12.4.23: Perform each of the following elementary row operations on the augm...
 12.12.1.23: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.23: Evaluate each determinant. See Example 1. ` ` 9 110 5 `
 12.12.2.24: Solve each system. See Example 3. 5x 6z 4y 219x 2y 3z 473x y 19
 12.24: Write a system of two equations in two variables to solve each prob...
 12.12.3.24: Mixing Nuts. The owner of a candy store wants to mix some peanuts w...
 12.12.4.24: Perform each of the following elementary row operations on the augm...
 12.12.1.24: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.24: Evaluate each determinant. See Example 1. `7 76 4 ` `
 12.12.2.25: Solve each system. See Example 3. 2x z 2 y8x 3y 26x 2y 3z 4
 12.25: Write a system of two equations in two variables to solve each prob...
 12.12.3.25: Piggy Banks. When a child breaks open her piggy bank, she finds a t...
 12.12.4.25: Use matrices to solve each system of equations. See Example 3. ex y...
 12.12.1.25: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.25: Evaluate each determinant. See Example 1. ` ` 8 89 9 `
 12.12.2.26: Solve each system. See Example 3. 3y z 1x 2z 9 6y9y 3z 9 2x
 12.26: Write a system of two equations in two variables to solve each prob...
 12.12.3.26: Theater Seating. The illustration shows the cash receipts and the t...
 12.12.4.26: Use matrices to solve each system of equations. See Example 3. ex y...
 12.12.1.26: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.26: Evaluate each determinant. See Example 1. `20 320 3 `
 12.12.2.27: Solve each system using elimination. See Example 4. x y 3z 35x 3y 2...
 12.27: Use a check to determine whether is a solution of the system: x y z...
 12.12.3.27: Astronomy. Comets have elliptical orbits, but the orbits of some co...
 12.12.4.27: Use matrices to solve each system of equations. See Example 3. e2x ...
 12.12.1.27: Solve each system by graphing. See Example 5. 16x 13y12y x
 12.12.5.27: Evaluate each determinant. See Examples 2 and 3. 321412531
 12.12.2.28: Solve each system using elimination. See Example 4. x 2y 3z 115x y ...
 12.28: A system of three linear equations in three variables is graphed on...
 12.12.3.28: Curve Fitting. Find an equation of the form y ax2 bx c for the para...
 12.12.4.28: Use matrices to solve each system of equations. See Example 3. e5x ...
 12.12.1.28: Solve each system by graphing. See Example 5. x y 314x 16y 131
 12.12.5.28: Evaluate each determinant. See Examples 2 and 3. 623154235
 12.12.2.29: Solve each system using elimination. See Example 4. 3x 2y z 276x 3y...
 12.29: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.29: Walkways. A circular sidewalk is to be constructed in a city park. ...
 12.12.4.29: Use matrices to solve each system of equations. See Example 4. x y ...
 12.12.1.29: Solve each system by graphing. See Example 5. 13x 76y 1215y 13x715x
 12.12.5.29: Evaluate each determinant. See Examples 2 and 3. 1 2 32 113 2 1
 12.12.2.30: Solve each system using elimination. See Example 4. 2x y 4x 2y 8z 7...
 12.30: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.30: Curve Fitting. The equation of a circle is of the form x2 y2 Cx Dy ...
 12.12.4.30: Use matrices to solve each system of equations. See Example 4. x y ...
 12.12.1.30: Solve each system by graphing. See Example 5. 35x14y 111018x 132413y
 12.12.5.30: Evaluate each determinant. See Examples 2 and 3. 11 22 1 231 3
 12.12.2.31: Solve each system using substitution. See Example 5. r s 3t 21r 4s ...
 12.31: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.31: Explain why the following problem does not give enough information ...
 12.12.4.31: Use matrices to solve each system of equations. See Example 4. 3x y...
 12.12.1.31: Use a graphing calculator to solve each system. Give all answers to...
 12.12.5.31: Evaluate each determinant. See Examples 2 and 3. 251034126
 12.12.2.32: Solve each system using substitution. See Example 5. r s 6t 12r 6s ...
 12.32: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.32: Write an application problem that can be solved using a system of t...
 12.12.4.32: Use matrices to solve each system of equations. See Example 4. 2x y...
 12.12.1.32: Use a graphing calculator to solve each system. Give all answers to...
 12.12.5.32: Evaluate each determinant. See Examples 2 and 3. 4 1 26 1 01 3 4
 12.12.2.33: Solve each system using substitution. See Example 5. x 8z 303x y 4z...
 12.33: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.33: Determine whether each equation defines to be a function of . If it...
 12.12.4.33: Use matrices to solve each system of equations. If the equations of...
 12.12.1.33: Use a graphing calculator to solve each system. Give all answers to...
 12.12.5.33: Evaluate each determinant. See Examples 2 and 3. 1 4 13 0 23 1 2
 12.12.2.34: Solve each system using substitution. See Example 5. x 6z 365x 3y 2...
 12.34: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.34: Determine whether each equation defines to be a function of . If it...
 12.12.4.34: Use matrices to solve each system of equations. If the equations of...
 12.12.1.34: Use a graphing calculator to solve each system. Give all answers to...
 12.12.5.34: Evaluate each determinant. See Examples 2 and 3. 8 3 11 023 9 4
 12.12.2.35: Solve each system. If a system is inconsistent or if the equations ...
 12.35: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.35: Determine whether each equation defines to be a function of . If it...
 12.12.4.35: Use matrices to solve each system of equations. If the equations of...
 12.12.1.35: Solve each system by substitution. See Example 6. ey 3xx y 8
 12.12.5.35: Evaluate each determinant. See Examples 2 and 3. 12 137 34 3 5
 12.12.2.36: Solve each system. If a system is inconsistent or if the equations ...
 12.36: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.3.36: Determine whether each equation defines to be a function of . If it...
 12.12.4.36: Use matrices to solve each system of equations. If the equations of...
 12.12.1.36: Solve each system by substitution. See Example 6. ey x 2x 2y 16 e
 12.12.5.36: Evaluate each determinant. See Examples 2 and 3. 147258369
 12.12.2.37: Solve each system. If a system is inconsistent or if the equations ...
 12.37: Teddy Bears. A toy company produces three sizes of teddy bears. Eac...
 12.12.3.37: Determine whether each equation defines to be a function of . If it...
 12.12.4.37: Use matrices to solve each system of equations. If the equations of...
 12.12.1.37: Solve each system by substitution. See Example 6. ex 2 y2x y 13
 12.12.5.37: Evaluate each determinant. See Examples 2 and 3. 120012001
 12.12.2.38: Solve each system. If a system is inconsistent or if the equations ...
 12.38: Financial Planning. A financial planner invested $22,000 in three a...
 12.12.3.38: Determine whether each equation defines to be a function of . If it...
 12.12.4.38: Use matrices to solve each system of equations. If the equations of...
 12.12.1.38: Solve each system by substitution. See Example 6. ex 5 y3x 2y 7 e
 12.12.5.38: Evaluate each determinant. See Examples 2 and 3. 101010111
 12.12.2.39: Solve each system, if possible. If a system is inconsistent or if t...
 12.39: Ballistics. The path of a thrown object is a parabola with an equat...
 12.12.3.39: Determine whether each equation defines to be a function of . If it...
 12.12.4.39: Use matrices to solve each system of equations. If the equations of...
 12.12.1.39: Solve each system by substitution. See Example 6. ex 2y 63x y 10
 12.12.5.39: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.40: Solve each system, if possible. If a system is inconsistent or if t...
 12.40: Veterinary Medicine. The daily requirements of a balanced diet for ...
 12.12.3.40: Determine whether each equation defines to be a function of . If it...
 12.12.4.40: Use matrices to solve each system of equations. If the equations of...
 12.12.1.40: Solve each system by substitution. See Example 6. e2x y 214x 5y 7 e
 12.12.5.40: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.41: Solve each system, if possible. If a system is inconsistent or if t...
 12.41: Represent each system of equations using an augmented matrix. e5x 4...
 12.12.3.41: Digits Problems. The sum of the digits of a threedigit number is 8...
 12.12.4.41: Use matrices to solve each system of equations. If the equations of...
 12.12.1.41: Solve each system by substitution. See Example 6. e5x 3y 263x y 14
 12.12.5.41: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.42: Solve each system, if possible. If a system is inconsistent or if t...
 12.42: Represent each system of equations using an augmented matrix. x 2y ...
 12.12.3.42: Purchasing Pets. A pet store owner spent $100 to buy 100 animals. H...
 12.12.4.42: Use matrices to solve each system of equations. If the equations of...
 12.12.1.42: Solve each system by substitution. See Example 6. e3x 5y 45x y 14
 12.12.5.42: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.43: Solve each system, if possible. If a system is inconsistent or if t...
 12.43: Perform each of the following elementary row operations on the augm...
 12.12.4.43: Use matrices to solve each system of equations. If the equations of...
 12.12.1.43: Solve each system by elimination (addition). See Example 7. ex y 7x...
 12.12.5.43: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.44: Solve each system, if possible. If a system is inconsistent or if t...
 12.44: Perform each of the following elementary row operations on the augm...
 12.12.4.44: Use matrices to solve each system of equations. If the equations of...
 12.12.1.44: Solve each system by elimination (addition). See Example 7. ea b 5a...
 12.12.5.44: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.45: Solve each system, if possible. If a system is inconsistent or if t...
 12.45: Solve each system using matrices, if possible. If a system is incon...
 12.12.4.45: Use matrices to solve each system of equations. If the equations of...
 12.12.1.45: Solve each system by elimination (addition). See Example 7. e2s 3t ...
 12.12.5.45: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.46: Solve each system, if possible. If a system is inconsistent or if t...
 12.46: Solve each system using matrices, if possible. If a system is incon...
 12.12.4.46: Use matrices to solve each system of equations. If the equations of...
 12.12.1.46: Solve each system by elimination (addition). See Example 7. ex 2y 2...
 12.12.5.46: Use Cramers rule to solve each system of equations. See Example 4. ...
 12.12.2.47: Solve each system, if possible. If a system is inconsistent or if t...
 12.47: Solve each system using matrices, if possible. If a system is incon...
 12.12.4.47: Use matrices to solve each system of equations. If the equations of...
 12.12.1.47: Solve each system by elimination (addition). See Example 7. e3x 4y ...
 12.12.5.47: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.48: Solve each system, if possible. If a system is inconsistent or if t...
 12.48: Solve each system using matrices, if possible. If a system is incon...
 12.12.4.48: Use matrices to solve each system of equations. If the equations of...
 12.12.1.48: Solve each system by elimination (addition). See Example 7. e5x 2y ...
 12.12.5.48: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.49: Solve each system, if possible. If a system is inconsistent or if t...
 12.49: Evaluate each determinant. 2 34 3 `
 12.12.4.49: Use matrices to solve each system of equations. If the equations of...
 12.12.1.49: Solve each system by elimination (addition). See Example 7. 56x12 y...
 12.12.5.49: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.50: Solve each system, if possible. If a system is inconsistent or if t...
 12.50: Evaluate each determinant. `3 45 6 ` ` 2 3
 12.12.4.50: Use matrices to solve each system of equations. If the equations of...
 12.12.1.50: Solve each system by elimination (addition). See Example 7. 13x12 y...
 12.12.5.50: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.51: Solve each system, if possible. If a system is inconsistent or if t...
 12.51: Evaluate each determinant. 1 2 12 1 31 2 2
 12.12.4.51: Use matrices to solve each system of equations. If the equations of...
 12.12.1.51: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.5.51: Use Cramers rule to solve each system of equations. See Example 6. ...
 12.12.2.52: Solve each system, if possible. If a system is inconsistent or if t...
 12.52: Evaluate each determinant. 3 2 21 2 22 1 1
 12.12.4.52: Use matrices to solve each system of equations. If the equations of...
 12.12.1.52: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.5.52: Use Cramers rule to solve each system of equations. See Example 6. ...
 12.12.2.53: Solve each system, if possible. If a system is inconsistent or if t...
 12.53: Use Cramers rule to solve each system, if possible. If a system is ...
 12.12.4.53: Digital Photography. A digital camera stores the black and white ph...
 12.12.1.53: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.5.53: Use Cramers rule to solve each system of equations. See Example 6. ...
 12.12.2.54: Solve each system, if possible. If a system is inconsistent or if t...
 12.54: Use Cramers rule to solve each system, if possible. If a system is ...
 12.12.4.54: Digital Imaging. A scanner stores a black and white photograph as a...
 12.12.1.54: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.5.54: Use Cramers rule to solve each system of equations. See Example 6. ...
 12.12.2.55: Solve each system, if possible. If a system is inconsistent or if t...
 12.55: Use Cramers rule to solve each system, if possible. If a system is ...
 12.12.4.55: Complementary Angles. The following system can be used to find the ...
 12.12.1.55: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.55: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.56: Solve each system, if possible. If a system is inconsistent or if t...
 12.56: Use Cramers rule to solve each system, if possible. If a system is ...
 12.12.4.56: Supplementary Angles. The following system can be used to find the ...
 12.12.1.56: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.56: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.57: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.4.57: Triangles. The following system can be used to find the measures (i...
 12.12.1.57: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.57: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.58: Solve each system, if possible. If a system is inconsistent or if t...
 12.12.4.58: Triangles. The following system can be used to find the measures (i...
 12.12.1.58: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.58: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.59: Graphs of Systems. Explain how each of the following pictures is an...
 12.12.4.59: For the system e2x 3y 54x 8 y104, explain what is wrong with writin...
 12.12.1.59: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.59: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.60: Zoology. An Xray of a mouse revealed a cancerous tumor located at ...
 12.12.4.60: Explain what is meant by the phrase reduced rowechelon form. Give ...
 12.12.1.60: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.60: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.61: NBA Records. The three highest onegame point totals by one player ...
 12.12.4.61: Explain how a type 3 row operation is similar to the elimination (a...
 12.12.1.61: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.61: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.62: Bicycle Frames. The angle measures of the triangular part of the bi...
 12.12.4.62: If the system represented by the augmented matrix at the right has ...
 12.12.1.62: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.62: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.63: Explain how a system of three equations in three variables can be r...
 12.12.4.63: What is the formula used to find the slope of a line, given two poi...
 12.12.1.63: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.63: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.64: What makes a system of three equations with three variables inconsi...
 12.12.4.64: What is the form of the equation of a horizontal line? Of a vertica...
 12.12.1.64: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.64: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.65: What does the graph of a linear equation in three variables such as...
 12.12.4.65: What is the pointslope form of the equation of a line?
 12.12.1.65: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.65: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.66: What situation discussed in this section looks like two walls of a ...
 12.12.4.66: What is the slopeintercept form of the equation of a line?
 12.12.1.66: Solve each system by graphing, if possible. If a system is inconsis...
 12.12.5.66: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.67: Graph each of the basic functions. (x) x
 12.12.4.67: Use matrices to solve the system. x2 y2 z2 142x2 3y2 2z2 7x2 5y2 z2...
 12.12.1.67: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.67: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.68: Graph each of the basic functions. g(x) x2
 12.12.4.68: Use matrices to solve the system. w x y z 0w 2x y 3z 32w 3x y 2z 12...
 12.12.1.68: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.68: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.69: Graph each of the basic functions. h(x) x 3
 12.12.1.69: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.69: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.70: Graph each of the basic functions. S(x) x
 12.12.1.70: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.70: Use Cramers rule to solve each system of equations. If a system is ...
 12.12.2.71: Solve each system. w x y z 3w x y z 1w x y z 1w x y z 3
 12.12.1.71: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.71: Use a calculator with matrix capabilities. Evaluate each determinan...
 12.12.2.72: Solve each system. 1x1y1z 32x1y 1z 01x 2y4z 21
 12.12.1.72: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.72: Use a calculator with matrix capabilities. Evaluate each determinan...
 12.12.5.73: Use a calculator with matrix capabilities. Evaluate each determinan...
 12.12.2.73: Solve each system. 4a b 2c 3d 163a 3b c 4d 20a 2b 5c d 45a 4b 3c d 10
 12.12.1.73: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.74: Use a calculator with matrix capabilities. Evaluate each determinan...
 12.12.2.74: Solve each system. a c 2d 4b 2c 1a 2b c 22a b 3c 2d 4
 12.12.1.74: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.75: Signaling. Solve the following system using Cramers rule to find th...
 12.12.1.75: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.76: Investing. Solve the following system using Cramers rule to find th...
 12.12.1.76: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.77: Explain the difference between a matrix and a determinant. Give an ...
 12.12.1.77: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.78: When evaluating 4 1 26 1 01 3 4 , why is it helpful to expand by th...
 12.12.1.78: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.79: Explain how to find the minor of an element of a determinant.
 12.12.1.79: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.80: Explain how to find when solving a system of three linear equations...
 12.12.1.80: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.81: Explain how the following checkerboard pattern is used when evaluat...
 12.12.1.81: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.82: Briefly describe each of the five methods of this chapter that can ...
 12.12.1.82: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.83: Are the lines described by y 2x 7 and x 2y 7 perpendicular?
 12.12.1.83: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.84: Are the lines described by y 2x 7 2x and 2x y 10y parallel?
 12.12.1.84: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.85: How are the graphs of (x) x2 and g(x) x2 x related?
 12.12.1.85: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.86: Is the graph of a circle the graph of a function?
 12.12.1.86: Solve each system by any method. If a system is inconsistent or if ...
 12.12.5.87: The graph of a line passes through (0, 3). Is this the xintercept ...
 12.12.1.87: Solve each system. To do so, substitute a for 1xand b for 1yand sol...
 12.12.5.88: What is the name of the function (x) 0 x 0?
 12.12.1.88: Solve each system. To do so, substitute a for 1xand b for 1yand sol...
 12.12.5.89: For the function y 2x2 6x 1, what is the independent variable and w...
 12.12.1.89: Solve each system. To do so, substitute a for 1xand b for 1yand sol...
 12.12.5.90: If (x) x 3 x, what is (1) 3 ?
 12.12.1.90: Solve each system. To do so, substitute a for 1xand b for 1yand sol...
 12.12.5.91: Show that x y 1231351 0 represents the equation of the line passing...
 12.12.1.91: Fashion Designer One of the line graphs below gives the percent sha...
 12.12.5.92: Show that 12 001301041 represents the area of the triangle with ver...
 12.12.1.92: The Internet. The graph on the next page shows the growing importan...
 12.12.1.93: Law of Supply and Demand. The demand function, graphed below, descr...
 12.12.1.94: Cost and Revenue. The function C(x) 200x 400 gives the cost for a c...
 12.12.1.95: Business. Estimate the breakeven point (where cost revenue) on the...
 12.12.1.96: Navigation. The paths of two ships are tracked on the same coordina...
 12.12.1.97: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.98: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.99: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.100: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.101: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.102: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.103: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.104: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.105: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.106: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.107: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.108: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.109: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.110: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.111: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.112: In Exercises 97112, write a system of two equations in two variable...
 12.12.1.113: Which method would you use to solve the system? Explain. ey 1 3x3x ...
 12.12.1.114: Which method would you use to solve the system? Explain. e2x 4y 93x...
 12.12.1.115: When solving a system, what advantages are there with the substitut...
 12.12.1.116: When using the elimination (addition) method, how can you tell whet...
 12.12.1.117: Solve each formula for the specified variable. V2V1 P1P2 for P1
 12.12.1.118: Solve each formula for the specified variable. 1r 1r11r2for r
 12.12.1.119: Solve each formula for the specified variable. S r a lr1 r for r
 12.12.1.120: Solve each formula for the specified variable. P Q1Q1Q2 for Q1
 12.12.1.121: If the solution of the system Ax By 2Bx Ay 26P is (3, 5), find the ...
 12.12.1.122: Solve and assume that and are constants. e db 2ab 3cd 1 3ab 2cd 1 A
Solutions for Chapter 12: More on Systems of Equations
Full solutions for Elementary and Intermediate Algebra  5th Edition
ISBN: 9781111567682
Solutions for Chapter 12: More on Systems of Equations
Get Full SolutionsSince 454 problems in chapter 12: More on Systems of Equations have been answered, more than 69520 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5. Chapter 12: More on Systems of Equations includes 454 full stepbystep solutions. Elementary and Intermediate Algebra was written by and is associated to the ISBN: 9781111567682. This expansive textbook survival guide covers the following chapters and their solutions.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column space C (A) =
space of all combinations of the columns of A.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.