 3.3.1.1: a. Estimate the coordinates of the point of intersection on the acc...
 3.3.2.1: a. Match each system of linear equations with the graph of the syst...
 3.3.3.1: On different grids, graph and shade in the areas described by the f...
 3.3.4.1: Match each function with its graph. a. f (x) 5 e x if x # 2 2x 1 4 ...
 3.1: The following graph shows worldwide production and consumption of g...
 3.3.1.2: a. Determine whether (2, 3) is a solution for the following system ...
 3.3.2.2: . Predict the number of solutions to each of the following systems....
 3.3.3.2: On different grids, graph and shade in the areas described by the f...
 3.3.4.2: Construct a piecewise linear function for each of the accompanying ...
 3.2: The accompanying graphs show two systems of linear equations. For e...
 3.3.1.3: a. Estimate the solution to the system of linear equations graphed ...
 3.3.2.3: For each system: a. Indicate whether the substitution or eliminatio...
 3.3.3.3: Use inequalities to describe each shaded region.
 3.3.4.3: a. Graph the following functions on the same grid. j(x) 5 x b. Esti...
 3.3: a. Construct a system of linear equations where both of the followi...
 3.3.1.4: Determine which of the given ordered pairs is a solution of the sys...
 3.3.2.4: For each graph, construct the equations for each of the two lines i...
 3.3.3.4: Use inequalities to describe each shaded region.
 3.3.4.4: a. Construct a graduated tax function where the tax is 10% on the f...
 3.4: New York City taxi fares are listed in the following table: a. Crea...
 3.3.1.5: a. Find the equation of a line with slope 3 that goes through the p...
 3.3.2.5: a. Solve the following system algebraically: x 1 3y 5 6 5x 1 3y 5 2...
 3.3.3.5: On different grids, graph each inequality (shading in the appropria...
 3.3.4.5: You are thinking about replacing your longdistance telephone servi...
 3.5: Graph and shade the region bounded by the following inequalities: y...
 3.3.1.6: Examine the graphs of three systems below. a. What do the three sys...
 3.3.2.6: Calculate the solution(s), if any, to each of the following systems...
 3.3.3.6: Determine whether or not the point (21, 3) satisfies the inequality...
 3.3.4.6: Graphing program recommended). In 2004, Missouri had a graduated ta...
 3.6: Determine the inequalities that describe the shaded region in the f...
 3.3.1.7: Construct a sketch of each system by hand and then estimate the sol...
 3.3.2.7: . Assume you have $2000 to invest for 1 year. You can make a safe i...
 3.3.3.7: Explain how you can tell if the region described by the inequality ...
 3.3.4.7: Heart health is a prime concern, because heart disease is the leadi...
 3.7: A musician produces and sells CDs on her website. She estimates fix...
 3.3.1.8: For the linear system a. Graph the system. Estimate the solution fo...
 3.3.2.8: Two investments in hightechnology companies total $1000. If one in...
 3.3.3.8: Shade the region bounded by the inequalities y $ 0 x $ 0 2x 1 y # 1...
 3.3.4.8: A graduated income tax is proposed in Borduria to replace an existi...
 3.8: Data from the U.S. Department of Energy show that gasoline prices v...
 3.9: The graph below shows the production and consumption of oil from 19...
 3.3.1.9: Create the system of equations that produced the accompanying graph...
 3.3.2.9: Solve the following systems: a. b. x 2 x 2 y 5 y 5 4 3 1 y 5 9 x 4 ...
 3.3.3.9: Match each description in parts (a) to (e) with the appropriate com...
 3.3.4.9: It is often said that 1 year of a dogs life is equivalent to 7 year...
 3.10: You keep track of how much gas your car uses and estimate that it g...
 3.3.1.10: The U.S. Bureau of Labor Statistics reports on the percent of all m...
 3.3.2.10: For each of the following systems of equations, describe the graph ...
 3.3.3.10: For the inequalities y 4x 3 and y 3x 4: a. Graph the two boundary l...
 3.3.4.10: You check around for the best deal on your prescription medicine. A...
 3.11: a. Solve algebraically each of the following systems of linear equa...
 3.3.1.11: The figure on the next page shows graphs of population growth in se...
 3.3.2.11: If y 5 b 1 mx, solve for values of m and b by constructing two line...
 3.3.3.11: Examine the shaded region in the graph. a. Create equations for the...
 3.12: Use the table to answer the following questions. Your goal is to ru...
 3.3.1.12: The accompanying figure shows the heights of two balloons at t hour...
 3.3.2.12: . The following are formulas predicting future raises for four diff...
 3.3.3.12: Examine the shaded region in the graph. Determine the compound ineq...
 3.13: Use the table to answer the following questions. Your goal is to ru...
 3.3.1.13: The graph at top of the next column shows changes in how health car...
 3.3.2.13: The supply and demand equations for a particular bicycle model rela...
 3.3.3.13: The Food and Drug Administration labels suntan products with a sun ...
 3.14: In a 400meter relay swim, each team has four swimmers. In sequence...
 3.3.1.14: The accompanying graphs show net debt as a percentage of gross dome...
 3.3.2.14: For a certain model of DVD player, the following supply and demand ...
 3.3.3.14: (Access to Internet required for part (c).) Doctors measure two kin...
 3.15: The accompanying table lists the monthly charge, the number of minu...
 3.3.1.15: Two companies offer starting employees incentives to stay with the ...
 3.3.2.15: Explain what is meant by two equivalent equations. Give an example ...
 3.3.3.15: (Graphing program recommended.) The blood alcohol concentration (BA...
 3.16: Suppose a flat tax amounts to 10% of income. Suppose a graduated ta...
 3.3.1.16: In the text the following cost equations were given for gas and sol...
 3.3.2.16: Without graphing each system of equations (at the top of the next c...
 3.3.3.16: (Graphing program recommended.) The Ontario Association of Sport an...
 3.17: The time series at the bottom of the page shows the price per barre...
 3.3.1.17: Answer the questions in Exercise 16 (with suitable changes in wordi...
 3.3.2.17: A restaurant is located on ground that slopes up 1 foot for every 2...
 3.3.3.17: Graphing program recommended.) We saw in Example 1 in this section ...
 3.18: Older toilets use about 7 gallons per flush. Since using this much ...
 3.3.1.18: Consider the following job offers. At Acme Corporation, you are off...
 3.3.2.18: A house attic as shown has a roofline with a slope of 5up for every...
 3.3.3.18: Cotton and wool fabrics, unless they have been preshrunk, will shri...
 3.19: Regular aerobic exercise at a target heart rate is recommended for ...
 3.3.1.19: a. Solve the following system algebraically: b. Graph the system in...
 3.3.2.19: Solve the following system of three equations in three variables, u...
 3.3.3.19: (Graphing program required.) Two professors from Purdue University ...
 3.20: . In the graph to the right, the Energy Information Administration ...
 3.3.1.20: While solar energy powered home systems are quite expensive to inst...
 3.3.2.20: Using the strategy described in Exercise 19, solve the following sy...
 3.3.3.20: (Graphing program required.) A company manufactures a particular mo...
 3.21: If the revenue per unit increases, and hence, R, the revenue line, ...
 3.3.1.21: In a previous exercise in Section 2.7, you read of a math professor...
 3.3.2.21: a. Construct a system of linear equations in two variables that has...
 3.3.3.21: Describe the shaded region in each graph with the appropriate inequ...
 3.22: If 700 units are produced and sold, the company is making about a $...
 3.3.2.22: Nenuphar wants to invest a total of $30,000 into two savings accoun...
 3.3.3.22: Describe the shaded region.
 3.23: A 15yearold girl who weighs 110 pounds and is 55 inches tall has ...
 3.3.2.23: When will the following system of equations have no solution? Justi...
 3.3.3.23: A financial advisor has up to $30,000 to invest, with the stipulati...
 3.24: . A 10yearold girl with BMI 5 12 is underweight for her height an...
 3.3.2.24: a. Construct a system of linear equations where both of the followi...
 3.3.3.24: A Texas oil supplier ships at most 10,000 barrels of oil per week. ...
 3.25: A mathematical description of the normal BMI zone for girls age 715...
 3.3.2.25: Lifeanddeath travel problems are dealt with by air traffic comput...
 3.3.3.25: A small Tshirt company created the following cost and revenue equa...
 3.26: Questions 26 and 27 refer to the following system of linear inequal...
 3.3.2.26: a. Examine the accompanying figure, where the demand curve has been...
 3.3.3.26: A large wholesale nursery sells shrubs to retail stores. The cost C...
 3.27: Questions 26 and 27 refer to the following system of linear inequal...
 3.3.2.27: a. Examine the accompanying figure at the top of the next page. Doe...
 3.3.3.27: The accompanying graph compares the total energy production, P(t), ...
 3.28: Linear systems of equations in two variables always have exactly on...
 3.3.2.28: In studying populations (human or otherwise), the two primary facto...
 3.3.3.28: The accompanying graph shows supply, S(q), and demand curves, D(q),...
 3.29: Any solution(s) to a linear system of equations in two variables is...
 3.3.2.29: Use the information in Exercise 28 to answer the following question...
 3.3.3.29: The following graph represents the percent of land in California af...
 3.30: Solutions to a linear system of inequalities in two variables can b...
 3.31: In 3136, give an example of a function or functions with the specif...
 3.32: In 3136, give an example of a function or functions with the specif...
 3.33: In 3136, give an example of a function or functions with the specif...
 3.34: In 3136, give an example of a function or functions with the specif...
 3.35: In 3136, give an example of a function or functions with the specif...
Solutions for Chapter 3: WHEN LINES MEET: LINEAR SYSTEMS
Full solutions for Explorations in College Algebra  5th Edition
ISBN: 9780470466445
Solutions for Chapter 3: WHEN LINES MEET: LINEAR SYSTEMS
Get Full SolutionsChapter 3: WHEN LINES MEET: LINEAR SYSTEMS includes 124 full stepbystep solutions. Since 124 problems in chapter 3: WHEN LINES MEET: LINEAR SYSTEMS have been answered, more than 8234 students have viewed full stepbystep solutions from this chapter. Explorations in College Algebra was written by and is associated to the ISBN: 9780470466445. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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!).

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.

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

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).