 10.1: determine the order of each matrix.
 10.2: determine the order of each matrix.
 10.3: determine the order of each matrix.
 10.4: determine the order of each matrix.
 10.5: determine the order of each matrix.
 10.6: determine the order of each matrix.
 10.7: write the augmented matrix for each system of linear equations.
 10.8: write the augmented matrix for each system of linear equations.
 10.9: write the augmented matrix for each system of linear equations.
 10.10: write the augmented matrix for each system of linear equations.
 10.11: write the augmented matrix for each system of linear equations.
 10.12: write the augmented matrix for each system of linear equations.
 10.13: write the augmented matrix for each system of linear equations.
 10.14: write the augmented matrix for each system of linear equations.
 10.15: write the system of linear equations represented by the augmented m...
 10.16: write the system of linear equations represented by the augmented m...
 10.17: write the system of linear equations represented by the augmented m...
 10.18: write the system of linear equations represented by the augmented m...
 10.19: write the system of linear equations represented by the augmented m...
 10.20: write the system of linear equations represented by the augmented m...
 10.21: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.22: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.23: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.24: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.25: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.26: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.27: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.28: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.29: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.30: indicate whether each matrix is in rowechelon form. If it is,determ...
 10.31: perform the indicated row operations on each augmented matrix.
 10.32: perform the indicated row operations on each augmented matrix.
 10.33: perform the indicated row operations on each augmented matrix.
 10.34: perform the indicated row operations on each augmented matrix.
 10.35: perform the indicated row operations on each augmented matrix.
 10.36: perform the indicated row operations on each augmented matrix.
 10.37: perform the indicated row operations on each augmented matrix.
 10.38: perform the indicated row operations on each augmented matrix.
 10.39: perform the indicated row operations on each augmented matrix.
 10.40: perform the indicated row operations on each augmented matrix.
 10.41: use row operations to transform each matrix to reduced rowechelon f...
 10.42: use row operations to transform each matrix to reduced rowechelon f...
 10.43: use row operations to transform each matrix to reduced rowechelon f...
 10.44: use row operations to transform each matrix to reduced rowechelon f...
 10.45: use row operations to transform each matrix to reduced rowechelon f...
 10.46: use row operations to transform each matrix to reduced rowechelon f...
 10.47: use row operations to transform each matrix to reduced rowechelon f...
 10.48: use row operations to transform each matrix to reduced rowechelon f...
 10.49: use row operations to transform each matrix to reduced rowechelon f...
 10.50: use row operations to transform each matrix to reduced rowechelon f...
 10.51: solve the system of linear equations using Gaussian elimination wit...
 10.52: solve the system of linear equations using Gaussian elimination wit...
 10.53: solve the system of linear equations using Gaussian elimination wit...
 10.54: solve the system of linear equations using Gaussian elimination wit...
 10.55: solve the system of linear equations using Gaussian elimination wit...
 10.56: solve the system of linear equations using Gaussian elimination wit...
 10.57: solve the system of linear equations using Gaussian elimination wit...
 10.58: solve the system of linear equations using Gaussian elimination wit...
 10.59: solve the system of linear equations using Gaussian elimination wit...
 10.60: solve the system of linear equations using Gaussian elimination wit...
 10.61: solve the system of linear equations using Gaussian elimination wit...
 10.62: solve the system of linear equations using Gaussian elimination wit...
 10.63: solve the system of linear equations using Gaussian elimination wit...
 10.64: solve the system of linear equations using Gaussian elimination wit...
 10.65: solve the system of linear equations using Gaussian elimination wit...
 10.66: solve the system of linear equations using Gaussian elimination wit...
 10.67: solve the system of linear equations using Gaussian elimination wit...
 10.68: solve the system of linear equations using Gaussian elimination wit...
 10.69: solve the system of linear equations using Gaussian elimination wit...
 10.70: solve the system of linear equations using Gaussian elimination wit...
 10.71: solve the system of linear equations using GaussJordan elimination.
 10.72: solve the system of linear equations using GaussJordan elimination.
 10.73: solve the system of linear equations using GaussJordan elimination.
 10.74: solve the system of linear equations using GaussJordan elimination.
 10.75: solve the system of linear equations using GaussJordan elimination.
 10.76: solve the system of linear equations using GaussJordan elimination.
 10.77: solve the system of linear equations using GaussJordan elimination.
 10.78: solve the system of linear equations using GaussJordan elimination.
 10.79: solve the system of linear equations using GaussJordan elimination.
 10.80: solve the system of linear equations using GaussJordan elimination.
 10.81: solve the system of linear equations using GaussJordan elimination.
 10.82: solve the system of linear equations using GaussJordan elimination.
 10.83: solve the system of linear equations using GaussJordan elimination.
 10.84: solve the system of linear equations using GaussJordan elimination.
 10.85: solve the system of linear equations using GaussJordan elimination.
 10.86: solve the system of linear equations using GaussJordan elimination.
 10.87: Football. In Super Bowl XXXVIII, the New England Patriots defeated ...
 10.88: Basketball. In the 2004 Summer Olympics in Athens, Greece, the U.S....
 10.89: rely on a selection of Subway sandwiches whose nutrition informatio...
 10.90: rely on a selection of Subway sandwiches whose nutrition informatio...
 10.91: involve vertical motion and the effect of gravity on an object. Bec...
 10.92: involve vertical motion and the effect of gravity on an object. Bec...
 10.93: Data CurveFitting. The average number of minutes that a person spe...
 10.94: Data CurveFitting. The average age when a woman gets married has b...
 10.95: Chemistry/Pharmacy.A pharmacy receives an order for 100 milliliters...
 10.96: Chemistry/Pharmacy.A pharmacy receives an order for 60 grams of a 0...
 10.97: Business.A small company has an assembly line that produces three t...
 10.98: Business.A small company has an assembly line that produces three t...
 10.99: Money. Gary and Ginger decide to place $10,000 of their savings int...
 10.100: Money. Ginger talks Gary into putting less money in the money marke...
 10.101: Manufacturing.A company produces three products x, y, and z. Each i...
 10.102: Geometry. Find the values of a, b, and c such that the graph of the...
 10.103: Ticket Sales. One hundred students decide to buy tickets to a footb...
 10.104: Exercise and Nutrition.Ann would like to exercise one hour per day ...
 10.105: Geometry. The circle given by the equation x2 y2 ax by c 0 passes t...
 10.106: Geometry. The circle given by the equation x2 y2 ax by c 0 passes t...
 10.107: explain the mistake that is made.Solve the system of equations usin...
 10.108: explain the mistake that is made. Perform the indicated row operati...
 10.109: explain the mistake that is made.Solve the system of equations usin...
 10.110: explain the mistake that is made. Solve the system of equations usi...
 10.111: Determine whether each of the following statements is true or false...
 10.112: Determine whether each of the following statements is true or false...
 10.113: Determine whether each of the following statements is true or false...
 10.114: Determine whether each of the following statements is true or false...
 10.115: A fourthdegree polynomial f(x) ax4 bx3 cx2 dx e, with a 0, can be ...
 10.116: A copy machine accepts nickels, dimes, and quarters. After 1 hour, ...
 10.117: In Exercise 57, you were asked to solve this system of equations us...
 10.118: In Exercise 58, you were asked to solve this system of equations us...
 10.119: you are asked to model a set of three points with a quadratic funct...
 10.120: you are asked to model a set of three points with a quadratic funct...
 10.1: state the order of each matrix.
 10.2: state the order of each matrix.
 10.3: state the order of each matrix.
 10.4: state the order of each matrix.
 10.5: state the order of each matrix.
 10.6: state the order of each matrix.
 10.7: state the order of each matrix.
 10.8: state the order of each matrix.
 10.9: state the order of each matrix.
 10.10: state the order of each matrix.
 10.11: solve for the indicated variable.
 10.12: solve for the indicated variable.
 10.13: solve for the indicated variable.
 10.14: solve for the indicated variable.
 10.15: solve for the indicated variable.
 10.16: solve for the indicated variable.
 10.17: perform the indicated operations for each expression, if possible.
 10.18: perform the indicated operations for each expression, if possible.
 10.19: perform the indicated operations for each expression, if possible.
 10.20: perform the indicated operations for each expression, if possible.
 10.21: perform the indicated operations for each expression, if possible.
 10.22: perform the indicated operations for each expression, if possible.
 10.23: perform the indicated operations for each expression, if possible.
 10.24: perform the indicated operations for each expression, if possible.
 10.25: perform the indicated operations for each expression, if possible.
 10.26: perform the indicated operations for each expression, if possible.
 10.27: perform the indicated operations for each expression, if possible.
 10.28: perform the indicated operations for each expression, if possible.
 10.29: perform the indicated operations for each expression, if possible.
 10.30: perform the indicated operations for each expression, if possible.
 10.31: perform the indicated operations for each expression, if possible.A...
 10.32: perform the indicated operations for each expression, if possible.A...
 10.33: perform the indicated operations for each expression, if possible.A...
 10.34: perform the indicated operations for each expression, if possible.A...
 10.35: perform the indicated operations for each expression, if possible.A...
 10.36: perform the indicated operations for each expression, if possible.A...
 10.37: perform the indicated operations for each expression, if possible.A...
 10.38: perform the indicated operations for each expression, if possible.A...
 10.39: perform the indicated operations for each expression, if possible.A...
 10.40: perform the indicated operations for each expression, if possible.A...
 10.41: perform the indicated operations for each expression, if possible.A...
 10.42: perform the indicated operations for each expression, if possible.A...
 10.43: perform the indicated operations for each expression, if possible.A...
 10.44: perform the indicated operations for each expression, if possible.A...
 10.45: perform the indicated operations for each expression, if possible.A...
 10.46: perform the indicated operations for each expression, if possible.A...
 10.47: perform the indicated operations for each expression, if possible.A...
 10.48: perform the indicated operations for each expression, if possible.A...
 10.49: perform the indicated operations for each expression, if possible.A...
 10.50: perform the indicated operations for each expression, if possible.A...
 10.51: Smoking. On January 6 and 10, 2000, the Harris Poll conducted a sur...
 10.52: Women in Science.According to the study of science and engineering ...
 10.53: Registered Voters.According to the U.S. Census Bureau (www.census.g...
 10.54: Job Application.A company has two rubrics for scoring job applicant...
 10.55: Taxes. The IRS allows an individual to deduct business expenses in ...
 10.56: Tips on Service. Marilyn decides to go to the Safety Harbor Spa for...
 10.57: Use the following nutritional chart Nutrition. Utilize the table to...
 10.58: Use the following nutritional chart Nutrition. Don decides to lm a ...
 10.59: Use the following tables The following table gives fuel and electri...
 10.60: Use the following tables The following table gives fuel and electri...
 10.61: refer to the following:The results of a nutritional analysis of one...
 10.62: refer to the following:The results of a nutritional analysis of one...
 10.63: refer to the following:Cell phone companies charge users based on t...
 10.64: refer to the following:Cell phone companies charge users based on t...
 10.65: explain the mistake that is made.Multiply .Solution: Multiply corre...
 10.66: explain the mistake that is made. Multiply .Solution: Multiply usin...
 10.67: determine whether the statements are true or false. If and , then.
 10.68: determine whether the statements are true or false. If AB is dened,...
 10.69: determine whether the statements are true or false.AB is dened only...
 10.70: determine whether the statements are true or false.A B is dened onl...
 10.71: For , nd
 10.72: In order for A2mn to be dened, what condition (with respect to m an...
 10.73: For nd A, A2, A3, . . . . What is An?
 10.74: For nd A, A2, A3, . . . . What is An?
 10.75: If AmnBnp is dened, explain why (Amn Bnp)2 is not dened for .
 10.76: If Amn Bmn and Cnm, explain why , if . m Z
 10.77: apply a graphing utility to perform the indicated matrix operations...
 10.78: apply a graphing utility to perform the indicated matrix operations...
 10.79: apply a graphing utility to perform the indicated matrix operations...
 10.80: apply a graphing utility to perform the indicated matrix operations...
 10.81: apply a graphing utility to perform the indicated matrix operations...
 10.82: apply a graphing utility to perform the indicated matrix operations...
 10.1: write the system of linear equations as a matrix equation. (Do not ...
 10.2: write the system of linear equations as a matrix equation. (Do not ...
 10.3: write the system of linear equations as a matrix equation. (Do not ...
 10.4: write the system of linear equations as a matrix equation. (Do not ...
 10.5: write the system of linear equations as a matrix equation. (Do not ...
 10.6: write the system of linear equations as a matrix equation. (Do not ...
 10.7: write the system of linear equations as a matrix equation. (Do not ...
 10.8: write the system of linear equations as a matrix equation. (Do not ...
 10.9: determine whether B is the multiplicative inverse of A using AA1 I.
 10.10: determine whether B is the multiplicative inverse of A using AA1 I.
 10.11: determine whether B is the multiplicative inverse of A using AA1 I.
 10.12: determine whether B is the multiplicative inverse of A using AA1 I.
 10.13: determine whether B is the multiplicative inverse of A using AA1 I.
 10.14: determine whether B is the multiplicative inverse of A using AA1 I.
 10.15: determine whether B is the multiplicative inverse of A using AA1 I.
 10.16: determine whether B is the multiplicative inverse of A using AA1 I.
 10.17: determine whether B is the multiplicative inverse of A using AA1 I.
 10.18: determine whether B is the multiplicative inverse of A using AA1 I.
 10.19: nd A1, if possible.
 10.20: nd A1, if possible.
 10.21: nd A1, if possible.
 10.22: nd A1, if possible.
 10.23: nd A1, if possible.
 10.24: nd A1, if possible.
 10.25: nd A1, if possible.
 10.26: nd A1, if possible.
 10.27: nd A1, if possible.
 10.28: nd A1, if possible.
 10.29: nd A1, if possible.
 10.30: nd A1, if possible.
 10.31: nd A1, if possible.
 10.32: nd A1, if possible.
 10.33: apply matrix algebra to solve the system of linear equations.
 10.34: apply matrix algebra to solve the system of linear equations.
 10.35: apply matrix algebra to solve the system of linear equations.
 10.36: apply matrix algebra to solve the system of linear equations.
 10.37: apply matrix algebra to solve the system of linear equations.
 10.38: apply matrix algebra to solve the system of linear equations.
 10.39: apply matrix algebra to solve the system of linear equations.
 10.40: apply matrix algebra to solve the system of linear equations.
 10.41: apply matrix algebra to solve the system of linear equations.
 10.42: apply matrix algebra to solve the system of linear equations.
 10.43: apply matrix algebra to solve the system of linear equations.
 10.44: apply matrix algebra to solve the system of linear equations.
 10.45: apply matrix algebra to solve the system of linear equations.
 10.46: apply matrix algebra to solve the system of linear equations.
 10.47: NCAA. University of Florida apparel sales associated with the Final...
 10.48: NASCAR. Tony Stewart (NASCAR driver) often drives in two races in t...
 10.49: apply the following decoding scheme:The encoding matrix is . The en...
 10.50: apply the following decoding scheme:The encoding matrix is . The en...
 10.51: apply the following decoding scheme:The encoding matrix is . The en...
 10.52: apply the following decoding scheme:The encoding matrix is . The en...
 10.53: apply the following decoding scheme:The encoding matrix is . The en...
 10.54: apply the following decoding scheme:The encoding matrix is . The en...
 10.55: Refer to the following: The results of a nutritional analysis of on...
 10.56: Refer to the following: The results of a nutritional analysis of on...
 10.57: refer to the following: Cell phone companies charge users based on ...
 10.58: refer to the following: Cell phone companies charge users based on ...
 10.59: explain the mistake that is made.Find the inverse of .Solution:Writ...
 10.60: explain the mistake that is made. Find the inverse of A given that ...
 10.61: determine whether each statement is true or false. If , then .
 10.62: determine whether each statement is true or false.All square matric...
 10.63: For what values of x does the inverse of A not exist, given ?
 10.64: Let . Find
 10.65: Verify that is the inverse of, provided .
 10.66: Let and form the matrix [AI 2]. Apply row operations to transform i...
 10.67: Why does the square matrix not have an inverse?
 10.68: Why does the square matrix not have an inverse?
 10.69: apply a graphing utility to perform the indicated matrix operations...
 10.70: apply a graphing utility to perform the indicated matrix operations...
 10.71: apply a graphing utility and matrix algebra to solve the system of ...
 10.72: apply a graphing utility and matrix algebra to solve the system of ...
 10.73: apply a graphing utility and matrix algebra to solve the system of ...
 10.74: apply a graphing utility and matrix algebra to solve the system of ...
 10.1: evaluate each 2 2 determinant.
 10.2: evaluate each 2 2 determinant.
 10.3: evaluate each 2 2 determinant.
 10.4: evaluate each 2 2 determinant.
 10.5: evaluate each 2 2 determinant.
 10.6: evaluate each 2 2 determinant.
 10.7: evaluate each 2 2 determinant.
 10.8: evaluate each 2 2 determinant.
 10.9: evaluate each 2 2 determinant.
 10.10: evaluate each 2 2 determinant.
 10.11: use Cramers rule to solve each system of equations, if possible.
 10.12: use Cramers rule to solve each system of equations, if possible.
 10.13: use Cramers rule to solve each system of equations, if possible.
 10.14: use Cramers rule to solve each system of equations, if possible.
 10.15: use Cramers rule to solve each system of equations, if possible.
 10.16: use Cramers rule to solve each system of equations, if possible.
 10.17: use Cramers rule to solve each system of equations, if possible.
 10.18: use Cramers rule to solve each system of equations, if possible.
 10.19: use Cramers rule to solve each system of equations, if possible.
 10.20: use Cramers rule to solve each system of equations, if possible.
 10.21: use Cramers rule to solve each system of equations, if possible.
 10.22: use Cramers rule to solve each system of equations, if possible.
 10.23: use Cramers rule to solve each system of equations, if possible.
 10.24: use Cramers rule to solve each system of equations, if possible.
 10.25: use Cramers rule to solve each system of equations, if possible.
 10.26: use Cramers rule to solve each system of equations, if possible.
 10.27: use Cramers rule to solve each system of equations, if possible.
 10.28: use Cramers rule to solve each system of equations, if possible.
 10.29: use Cramers rule to solve each system of equations, if possible.
 10.30: use Cramers rule to solve each system of equations, if possible.
 10.31: use Cramers rule to solve each system of equations, if possible.
 10.32: use Cramers rule to solve each system of equations, if possible.
 10.33: evaluate each 3 3 determinant.
 10.34: evaluate each 3 3 determinant.
 10.35: evaluate each 3 3 determinant.
 10.36: evaluate each 3 3 determinant.
 10.37: evaluate each 3 3 determinant.
 10.38: evaluate each 3 3 determinant.
 10.39: evaluate each 3 3 determinant.
 10.40: evaluate each 3 3 determinant.
 10.41: evaluate each 3 3 determinant.
 10.42: evaluate each 3 3 determinant.
 10.43: evaluate each 3 3 determinant.
 10.44: evaluate each 3 3 determinant.
 10.45: evaluate each 3 3 determinant.
 10.46: evaluate each 3 3 determinant.
 10.47: apply Cramers rule to solve each system of equations, if possible.
 10.48: apply Cramers rule to solve each system of equations, if possible.
 10.49: apply Cramers rule to solve each system of equations, if possible.
 10.50: apply Cramers rule to solve each system of equations, if possible.
 10.51: apply Cramers rule to solve each system of equations, if possible.
 10.52: apply Cramers rule to solve each system of equations, if possible.
 10.53: apply Cramers rule to solve each system of equations, if possible.
 10.54: apply Cramers rule to solve each system of equations, if possible.
 10.55: apply Cramers rule to solve each system of equations, if possible.
 10.56: apply Cramers rule to solve each system of equations, if possible.
 10.57: apply Cramers rule to solve each system of equations, if possible.
 10.58: apply Cramers rule to solve each system of equations, if possible.
 10.59: apply Cramers rule to solve each system of equations, if possible.
 10.60: apply Cramers rule to solve each system of equations, if possible.
 10.61: the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y...
 10.62: the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y...
 10.63: the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y...
 10.64: the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y...
 10.65: Geometry.An equation of a line that passes through two points (x1, ...
 10.66: Geometry. If three points (x1, y1), (x2, y2), and (x3, y3) are coll...
 10.67: Electricity: Circuit Theory. The following equations come from circ...
 10.68: Electricity: Circuit Theory. The following equations come from circ...
 10.69: explain the mistake that is made.Evaluate the determinant .Solution...
 10.70: explain the mistake that is made.Evaluate the determinant .Solution...
 10.71: explain the mistake that is made. Solve the system of linear equati...
 10.72: explain the mistake that is made.Solve the system of linear equatio...
 10.73: determine whether each statement is true or false.The value of a de...
 10.74: determine whether each statement is true or false. If all the entri...
 10.75: determine whether each statement is true or false.32 6 4 0 2 8 4 0 ...
 10.76: determine whether each statement is true or false.3312 028 312
 10.77: Calculate the determinant .
 10.78: Calculate the determinant .
 10.79: Evaluate the determinant:
 10.80: For the system of equationsnd a that guarantees no unique solution.
 10.81: Show thatby expanding down the second column.
 10.82: Show that by expanding across the third row.
 10.83: Use a graphing utility to evaluate the determinants.Compare with yo...
 10.84: Use a graphing utility to evaluate the determinants.Compare with yo...
 10.85: Use a graphing utility to evaluate the determinants.
 10.86: Use a graphing utility to evaluate the determinants.
 10.87: apply Cramers rule to solve each system of equations and a graphing...
 10.88: apply Cramers rule to solve each system of equations and a graphing...
 10.1: Write the augmented matrix for each system of linear equations.
 10.2: Write the augmented matrix for each system of linear equations.
 10.3: Write the augmented matrix for each system of linear equations.
 10.4: Write the augmented matrix for each system of linear equations.
 10.5: Indicate whether each matrix is in rowechelon form. If it is, state...
 10.6: Indicate whether each matrix is in rowechelon form. If it is, state...
 10.7: Indicate whether each matrix is in rowechelon form. If it is, state...
 10.8: Indicate whether each matrix is in rowechelon form. If it is, state...
 10.9: Perform the indicated row operations on each matrix.
 10.10: Perform the indicated row operations on each matrix.
 10.11: Perform the indicated row operations on each matrix.
 10.12: Perform the indicated row operations on each matrix.
 10.13: Apply row operations to transform each matrix to reduced rowechelon...
 10.14: Apply row operations to transform each matrix to reduced rowechelon...
 10.15: Apply row operations to transform each matrix to reduced rowechelon...
 10.16: Apply row operations to transform each matrix to reduced rowechelon...
 10.17: Solve the system of linear equations using augmented matrices.
 10.18: Solve the system of linear equations using augmented matrices.
 10.19: Solve the system of linear equations using augmented matrices.
 10.20: Solve the system of linear equations using augmented matrices.
 10.21: Solve the system of linear equations using augmented matrices.
 10.22: Solve the system of linear equations using augmented matrices.
 10.23: Solve the system of linear equations using augmented matrices.
 10.24: Solve the system of linear equations using augmented matrices.
 10.25: Solve the system of linear equations using augmented matrices.
 10.26: Solve the system of linear equations using augmented matrices.
 10.27: Fitting a Curve to Data. The average number of ights on a commercia...
 10.28: Investment Portfolio. Danny and Paula decide to invest $20,000 of t...
 10.29: Calculate the given expression, if possible. A C
 10.30: Calculate the given expression, if possible.B A
 10.31: Calculate the given expression, if possible.B E
 10.32: Calculate the given expression, if possible. A D
 10.33: Calculate the given expression, if possible.2A D
 10.34: Calculate the given expression, if possible.3E B
 10.35: Calculate the given expression, if possible.2D 3A
 10.36: Calculate the given expression, if possible.3B 4E
 10.37: Calculate the given expression, if possible. 5A 2D
 10.38: Calculate the given expression, if possible.5B 4E
 10.39: Calculate the given expression, if possible.. AB
 10.40: Calculate the given expression, if possible. BC
 10.41: Calculate the given expression, if possible.DA
 10.42: Calculate the given expression, if possible.AD
 10.43: Calculate the given expression, if possible.BC E
 10.44: Calculate the given expression, if possible. DB
 10.45: Calculate the given expression, if possible.EC
 10.46: Calculate the given expression, if possible. CE
 10.47: Determine whether B is the multiplicative inverse of A using AA1 I.
 10.48: Determine whether B is the multiplicative inverse of A using AA1 I.
 10.49: Determine whether B is the multiplicative inverse of A using AA1 I.
 10.50: Determine whether B is the multiplicative inverse of A using AA1 I.
 10.51: Find A1, if it exists.
 10.52: Find A1, if it exists.
 10.53: Find A1, if it exists.
 10.54: Find A1, if it exists.
 10.55: Find A1, if it exists.
 10.56: Find A1, if it exists.
 10.57: Find A1, if it exists.
 10.58: Find A1, if it exists.
 10.59: Solve the system of linear equations using matrix algebra.
 10.60: Solve the system of linear equations using matrix algebra.
 10.61: Solve the system of linear equations using matrix algebra.
 10.62: Solve the system of linear equations using matrix algebra.
 10.63: Solve the system of linear equations using matrix algebra.
 10.64: Solve the system of linear equations using matrix algebra.
 10.65: Evaluate each 2 2 determinant.
 10.66: Evaluate each 2 2 determinant.
 10.67: Evaluate each 2 2 determinant.
 10.68: Evaluate each 2 2 determinant.
 10.69: Employ Cramers rule to solve each system of equations, if possible.
 10.70: Employ Cramers rule to solve each system of equations, if possible.
 10.71: Employ Cramers rule to solve each system of equations, if possible.
 10.72: Employ Cramers rule to solve each system of equations, if possible.
 10.73: Employ Cramers rule to solve each system of equations, if possible.
 10.74: Employ Cramers rule to solve each system of equations, if possible.
 10.75: Evaluate each 3 3 determinant.
 10.76: Evaluate each 3 3 determinant.
 10.77: Evaluate each 3 3 determinant.
 10.78: Evaluate each 3 3 determinant.
 10.79: Employ Cramers rule to solve each system of equations, if possible.
 10.80: Employ Cramers rule to solve each system of equations, if possible.
 10.81: Employ Cramers rule to solve each system of equations, if possible.
 10.82: Employ Cramers rule to solve each system of equations, if possible.
 10.83: Apply determinants to nd the area of a triangle with vertices (2, 4...
 10.84: If three points (x1, y1), (x2, y2), and (x3, y3) are collinear (lie...
 10.85: refer to the following: You are asked to model a set of three point...
 10.86: refer to the following: You are asked to model a set of three point...
 10.87: Apply a graphing utility to perform the indicated matrix operations...
 10.88: Apply a graphing utility to perform the indicated matrix operations...
 10.89: Apply a graphing utility and matrix algebra to solve the system of ...
 10.90: Apply a graphing utility and matrix algebra to solve the system of ...
 10.91: Apply Cramers rule to solve each system of equations and a graphing...
 10.92: Apply Cramers rule to solve each system of equations and a graphing...
 10.1: Write each of the following systems of linear equations as an augme...
 10.2: Write each of the following systems of linear equations as an augme...
 10.3: Write each of the following systems of linear equations as an augme...
 10.4: Write each of the following systems of linear equations as an augme...
 10.5: Perform the following row operations:J 135 27 1 3 20 K R2  2R1 ...
 10.6: Rewrite the following matrix in reduced rowechelon form:J2 11 11 ...
 10.7: solve the systems of linear equations using augmented matrices. 6x ...
 10.8: solve the systems of linear equations using augmented matrices. 3x ...
 10.9: Multiply the matrices, if possible. 1 2 5 0 13 d J 04 3 5 11
 10.10: Add the matrices, if possible.1 2 5 0 13 d +J 04 3 5 11
 10.11: Find the inverse of , if it exists
 10.12: Find the inverse of , if it exists.
 10.13: Find the inverse of , if it exists.
 10.14: Solve the system of linear equations with matrix algebra (inverses)...
 10.15: Solve the system of linear equations with matrix algebra (inverses)...
 10.16: Calculate the determinant.27 5 2 12
 10.17: Calculate the determinant.31 2 1 3 52 4 10
 10.18: solve the system of linear equations using Cramers rule. x 2y 1 x 3y 2
 10.19: solve the system of linear equations using Cramers rule. 3x 5y 2z 6...
 10.20: A company has two rubrics for scoring job applicants based on weigh...
 10.21: A college student inherits $15,000 from his favorite aunt. He decid...
 10.22: You are asked to model a set of three points with a quadratic funct...
 10.23: Apply a graphing utility and matrix algebra to solve the system of ...
 10.24: Apply Cramers rule to solve the system of equations and a graphing ...
 10.1: Solve by completing the square: x2 6x 11.
 10.2: Write an equation of a line that passes through the point (2, 5) an...
 10.3: Write the equation of a circle with center (3, 1) and passing throu...
 10.4: Determine whether the relation x2 y2 25 is a function.
 10.5: Determine whether the function is odd or even.
 10.6: For the function y 5(x 4)2, identify all of the transformations of ...
 10.7: Find the composite function , and state the domain, for f(x) x3 1 a...
 10.8: ind the inverse of the function
 10.9: Find the vertex of the parabola associated with the quadratic funct...
 10.10: Find a polynomial of minimum degree (there are many) that has the z...
 10.11: Use long division to nd the quotient Q(x) and the remainder r(x) of...
 10.12: Given the zero x 4i of the polynomial P(x) x4 2x3 x2 32x 240, deter...
 10.13: Find the vertical and horizontal asymptotes of the function .
 10.14: If $5400 is invested at 2.25% compounded continuously, how much is ...
 10.15: Use interval notation to express the domain of the function f(x) lo...
 10.16: Use the properties of logarithms to simplify the expression logp1.
 10.17: Give an exact solution to the logarithmic equation log5 (x 2) log5 ...
 10.18: If money is invested in a savings account earning 4% compounded con...
 10.19: Solve the following system of linear equations:2 x + 3y = 6 x =1.5...
 10.20: At the student union, one group of students bought 6 deluxe burgers...
 10.21: Maximize the objective function z 5x 7y, subject to the constraints...
 10.22: Solve the system with GaussJordan elimination. x  2 y + 3 z = 11 4...
 10.23: Given nd 2A CB
 10.24: Write the matrix equation, nd the inverse of the coefcient matrix, ...
 10.25: Apply Cramers rule to solve the system of equations. 7 x + 5 y = 1 ...
 10.26: Use a graphing calculator to graph the given polynomial. From the g...
 10.27: Given nd AB and (AB) 1. A = c 0 16 4 3 1 d B = J7 4 10 62
Solutions for Chapter 10: Matrices
Full solutions for Algebra and Trigonometry  3rd Edition
ISBN: 9780470648032
Solutions for Chapter 10: Matrices
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780470648032. Chapter 10: Matrices includes 507 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 3. Since 507 problems in chapter 10: Matrices have been answered, more than 59853 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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 ().

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.