 2.4.1: A problem requires finding the number of cars on a dealers lot. Whi...
 2.4.2: A problem requires finding the number of hours a lightbulb is on du...
 2.4.3: A problem requires finding the distance traveled in miles. Which wo...
 2.4.4: A problem requires finding the time in minutes. Which would not be ...
 2.4.5: Solve each problem. See Example 1.The product of 8, and a number in...
 2.4.6: Solve each problem. See Example 1.The product of 5, and 3 more than...
 2.4.7: Solve each problem. See Example 1.If 2 is added to five times a num...
 2.4.8: Solve each problem. See Example 1.If four times a number is added t...
 2.4.9: Solve each problem. See Example 1.If 2 is subtracted from a number ...
 2.4.10: Solve each problem. See Example 1.If 3 is added to a number and thi...
 2.4.11: Solve each problem. See Example 1.The sum of three times a number a...
 2.4.12: Solve each problem. See Example 1.If 4 is added to twice a number a...
 2.4.13: Pennsylvania and Ohio were the states with the most remaining drive...
 2.4.14: As of 2008, the two most highly watched episodes in the history of ...
 2.4.15: In August 2009, the U.S. Senate had a total of 98 Democrats and Rep...
 2.4.16: In August 2009, the total number of Democrats and Republicans in th...
 2.4.17: Bon Jovi and Bruce Springsteen had the two topgrossing North Ameri...
 2.4.18: The Toyota Camry was the topselling passenger car in the United St...
 2.4.19: In the 20082009 NBA regular season, the Boston Celtics won two more...
 2.4.20: In the 2008 regular baseball season, the Tampa Bay Rays won 33 fewe...
 2.4.21: A onecup serving of orange juice contains 3 mg less than four time...
 2.4.22: A onecup serving of pineapple juice has 9 more than three times as...
 2.4.23: In one day, a store sold as many DVDs as CDs. The total number of D...
 2.4.24: A workout that combines weight training and aerobics burns a total ...
 2.4.25: The worlds largest taco contained approximately 1 kg of onion for e...
 2.4.26: . As of 2005, the combined population of China and India was estima...
 2.4.27: The value of a Mint State63 (uncirculated) 1950 Jefferson nickel m...
 2.4.28: U.S. fivecent coins are made from a combination of two metals: nic...
 2.4.29: A recipe for wholegrain bread calls for 1 oz of rye flour for ever...
 2.4.30: A medication contains 9 mg of active ingredients for every 1 mg of ...
 2.4.31: An office manager booked 55 airline tickets, divided among three ai...
 2.4.32: A mathematics textbook editor spent 7.5 hr making telephone calls, ...
 2.4.33: A partylength submarine sandwich that is 59 in. long is cut into t...
 2.4.34: China earned a total of 100 medals at the 2008 Beijing Summer Olymp...
 2.4.35: Venus is 31.2 million mi farther from the sun than Mercury, while E...
 2.4.36: Together, Saturn, Jupiter, and Uranus have a total of 137 known sat...
 2.4.37: The sum of the measures of the angles of any triangle is . In trian...
 2.4.38: In triangle ABC, the measure of angle A is more than the measure of...
 2.4.39: The numbers on two consecutively numbered gym lockers have a sum of...
 2.4.40: The numbers on two consecutive checkbook checks have a sum of 357. ...
 2.4.41: Two pages that are backtoback in this book have 203 as the sum of...
 2.4.42: . Two apartments have numbers that are consecutive integers. The su...
 2.4.43: Find two consecutive even integers such that the lesser added to th...
 2.4.44: Find two consecutive odd integers such that twice the greater is 17...
 2.4.45: When the lesser of two consecutive integers is added to three times...
 2.4.46: If five times the lesser of two consecutive integers is added to th...
 2.4.47: If the sum of three consecutive even integers is 60, what is the fi...
 2.4.48: If the sum of three consecutive odd integers is 69, what is the thi...
 2.4.49: If 6 is subtracted from the third of three consecutive odd integers...
 2.4.50: If the first and third of three consecutive even integers are added...
 2.4.51: Find the measure of an angle whose complement is four times its mea...
 2.4.52: Find the measure of an angle whose complement is five times its mea...
 2.4.53: Find the measure of an angle whose supplement is eight times its me...
 2.4.54: Find the measure of an angle whose supplement is three times its me...
 2.4.55: Find the measure of an angle whose supplement measures 39 more than...
 2.4.56: Find the measure of an angle whose supplement measures 38 less than...
 2.4.57: Find the measure of an angle such that the difference between the m...
 2.4.58: Find the measure of an angle such that the sum of the measures of i...
 2.4.59: Use the given values to evaluate each expression.LW L = 6, W = 4
 2.4.60: Use the given values to evaluate each expression.rt; r = 25, t = 4.5
 2.4.61: Use the given values to evaluate each expression.2L + 2W; L = 8, W = 2
 2.4.62: Use the given values to evaluate each expression.1 2h1b + B2; h = 1...
Solutions for Chapter 2.4: An Introduction to Applications of Linear Equations
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 2.4: An Introduction to Applications of Linear Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Chapter 2.4: An Introduction to Applications of Linear Equations includes 62 full stepbystep solutions. Since 62 problems in chapter 2.4: An Introduction to Applications of Linear Equations have been answered, more than 40099 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Beginning Algebra was written by and is associated to the ISBN: 9780321673480.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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.

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

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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!).

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Outer product uv T
= column times row = rank one matrix.

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.