 7.7.1.920: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.798: In Exercises 14, find all numbers for which each rational expressio...
 7.7.1.873: Find all numbers for which x 7 x2 5x 36 is undefined.
 7.7.1.900: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.921: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.799: In Exercises 14, find all numbers for which each rational expressio...
 7.7.1.874: In Exercises 23, simplify each rational expression. x2 2x 3 x2 3x 2
 7.7.1.901: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.922: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.800: In Exercises 14, find all numbers for which each rational expressio...
 7.7.1.875: In Exercises 23, simplify each rational expression. 4x2 20x x2 4x 5
 7.7.1.902: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.923: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.801: In Exercises 14, find all numbers for which each rational expressio...
 7.7.1.876: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.903: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.924: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.802: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.877: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.904: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.925: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.803: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.878: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.905: In Exercises 16, solve each equation, inequality, or system of equa...
 7.7.1.926: In Exercises 17, solve each equation, inequality, or system of equa...
 7.7.1.804: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.879: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.906: In Exercises 79, graph each equation in a rectangular coordinate sy...
 7.7.1.927: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.805: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.880: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.907: In Exercises 79, graph each equation in a rectangular coordinate sy...
 7.7.1.928: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.806: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.881: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.908: In Exercises 79, graph each equation in a rectangular coordinate sy...
 7.7.1.929: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.807: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.882: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.909: In Exercises 1012, simplify each expression. 21 16 3(2 8)
 7.7.1.930: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.808: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.883: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.910: In Exercises 1012, simplify each expression. 4x5 2x2 3
 7.7.1.931: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.809: In Exercises 512, simplify each rational expression. If the rationa...
 7.7.1.884: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.911: In Exercises 1012, simplify each expression. 1 x 2 4 1 x CUMULATIVE...
 7.7.1.932: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.810: In Exercises 1317, multiply as indicated x2 4 12x 3x x 2
 7.7.1.885: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.912: In Exercises 1315, factor completely. 4x2 13x 3
 7.7.1.933: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.811: In Exercises 1317, multiply as indicated 5x 5 6 3x x2 x
 7.7.1.886: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.913: In Exercises 1315, factor completely. 4x2 20x 25
 7.7.1.934: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.812: In Exercises 1317, multiply as indicated x2 6x 9 x2 4 x 2 x 3
 7.7.1.887: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.914: In Exercises 1315, factor completely. 3x2 75
 7.7.1.935: In Exercises 816, perform the indicated operations. If possible, si...
 7.7.1.813: In Exercises 1317, multiply as indicated y2 2y 1 y2 1 2y2 y 1 5y 5
 7.7.1.888: In Exercises 416, perform the indicated operations. Simplify the re...
 7.7.1.915: In Exercises 1618, perform the indicated operations. (4x2 3x 2) (5x...
 7.7.1.936: In Exercises 1722, factor completely. 4x2 49 (Section 6.4, Example 1)
 7.7.1.814: In Exercises 1317, multiply as indicated 2y2 y 3 4y2 9 3y 3 5y 5y2
 7.7.1.889: In Exercises 1718, simplify each complex rational expression. 5 5 x...
 7.7.1.916: In Exercises 1618, perform the indicated operations. 8x6 12x4 4x2 4x2
 7.7.1.937: In Exercises 1722, factor completely. x3 3x2 x 3 (Section 6.5, Exam...
 7.7.1.815: In Exercises 1822, divide as indicated. x2 x 2 10 2x 4 5
 7.7.1.890: In Exercises 1718, simplify each complex rational expression. 1 x 1...
 7.7.1.917: In Exercises 1618, perform the indicated operations. x 6 x 2 2x 1 x 3
 7.7.1.938: In Exercises 1722, factor completely. 2x2 8x 42 (Section 6.5, Examp...
 7.7.1.816: In Exercises 1822, divide as indicated. 6x 2 x2 1 3x2 x x 1
 7.7.1.891: In Exercises 1921, solve each rational equation. 5 x 2 3 2 2 x 1 6
 7.7.1.918: You invested $4000, part at 5% and the remainder at 9% annual inter...
 7.7.1.817: In Exercises 1822, divide as indicated. 1 y2 8y 15 7 y 5
 7.7.1.939: In Exercises 1722, factor completely. x5 16x (Section 6.4, Example 4)
 7.7.1.892: In Exercises 1921, solve each rational equation. 3 y 5 1 4 y 2y 10
 7.7.1.919: A 68inch board is to be cut into two pieces. If one piece must be ...
 7.7.1.818: In Exercises 1822, divide as indicated. y2 y 42 y 3 y 7 (y 3)2
 7.7.1.940: In Exercises 1722, factor completely. x3 10x2 25x (Section 6.4, Exa...
 7.7.1.893: In Exercises 1921, solve each rational equation. 2 x 1 3 x2 1 1
 7.7.1.819: In Exercises 1822, divide as indicated. 8x 8y x2 x2 y2 x2
 7.7.1.941: In Exercises 1722, factor completely. x3 8 (Section 6.4, Example 8)
 7.7.1.894: Solve for a: R as a s .
 7.7.1.820: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.942: In Exercises 2325, graph each equation in a rectangular coordinate ...
 7.7.1.895: In still water, a boat averages 30 miles per hour. It takes the boa...
 7.7.1.821: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.943: In Exercises 2325, graph each equation in a rectangular coordinate ...
 7.7.1.896: One pipe can fill a hot tub in 20 minutes and a second pipe can fil...
 7.7.1.822: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.944: In Exercises 2325, graph each equation in a rectangular coordinate ...
 7.7.1.897: Park rangers catch, tag, and release 200 tule elk back into a wildl...
 7.7.1.823: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.945: Find the slope of the line passing through the points (1, 3) and (2...
 7.7.1.898: The triangles in the figure are similar. Find the length of the sid...
 7.7.1.824: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.946: Write the pointslope form of the equation of the line passing thro...
 7.7.1.899: The amount of current flowing in an electrical circuit varies inver...
 7.7.1.825: In Exercises 2328, add or subtract as indicated. Simplify the resul...
 7.7.1.947: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.826: In Exercises 2931, find the least common denominator of the rationa...
 7.7.1.948: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.827: In Exercises 2931, find the least common denominator of the rationa...
 7.7.1.949: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.828: In Exercises 2931, find the least common denominator of the rationa...
 7.7.1.950: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.829: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.951: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.830: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.952: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.831: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.953: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.832: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.954: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.833: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.955: In Exercises 2836, use an equation or a system of equations to solv...
 7.7.1.834: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.835: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.836: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.837: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.838: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.839: In Exercises 3242, add or subtract as indicated. Simplify the resul...
 7.7.1.840: In Exercises 4347, simplify each complex rational expression. 1 2 3...
 7.7.1.841: In Exercises 4347, simplify each complex rational expression. 1 x 1...
 7.7.1.842: In Exercises 4347, simplify each complex rational expression. 1 x 1...
 7.7.1.843: In Exercises 4347, simplify each complex rational expression. 1 x 1...
 7.7.1.844: In Exercises 4347, simplify each complex rational expression. 3 12 ...
 7.7.1.845: In Exercises 4855, solve each rational equation. 3 x 1 6 1 x
 7.7.1.846: In Exercises 4855, solve each rational equation. 3 4x 1 x 1 4
 7.7.1.847: In Exercises 4855, solve each rational equation. x 5 6 x
 7.7.1.848: In Exercises 4855, solve each rational equation. 4 x x 5 5 x 5
 7.7.1.849: In Exercises 4855, solve each rational equation. 2 x 3 4 x 3 8 x2 9
 7.7.1.850: In Exercises 4855, solve each rational equation. 2 x 2 3 x 6
 7.7.1.851: In Exercises 4855, solve each rational equation. 13 y 1 3 1 y 1
 7.7.1.852: In Exercises 4855, solve each rational equation. 1 x 3 1 x 1 x 1 x2...
 7.7.1.853: Park rangers introduce 50 elk into a wildlife preserve. The formula...
 7.7.1.854: The formula S C 1 r describes the selling price, S, of a product in...
 7.7.1.855: In Exercises 5862, solve each formula for the specified variable. P...
 7.7.1.856: In Exercises 5862, solve each formula for the specified variable. P...
 7.7.1.857: In Exercises 5862, solve each formula for the specified variable. T...
 7.7.1.858: In Exercises 5862, solve each formula for the specified variable. 1...
 7.7.1.859: In Exercises 5862, solve each formula for the specified variable. I...
 7.7.1.860: In still water, a paddle boat averages 20 miles per hour. It takes ...
 7.7.1.861: A car travels 60 miles in the same time that a car traveling 10 mil...
 7.7.1.862: each car? 65. A painter can paint a fence around a house in 6 hours...
 7.7.1.863: If a school board determines that there should be 3 teachers for ev...
 7.7.1.864: To determine the number of trout in a lake, a conservationist catch...
 7.7.1.865: The triangles shown in the figure are similar. Find the length of t...
 7.7.1.866: Find the height of the lamppost in the figure. 6 ft 9 ft 5 ft ft
 7.7.1.867: A companys profit varies directly as the number of products it sell...
 7.7.1.868: The distance that a body falls from rest varies directly as the squ...
 7.7.1.869: The pitch of a musical tone varies inversely as its wavelength. A t...
 7.7.1.870: The loudness of a stereo speaker, measured in decibels, varies inve...
 7.7.1.871: The time required to assemble computers varies directly as the numb...
 7.7.1.872: The volume of a pyramid varies jointly as its height and the area o...
Solutions for Chapter 7: Chapter 7 Review Exercises
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 7: Chapter 7 Review Exercises
Get Full SolutionsThis textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. Chapter 7: Chapter 7 Review Exercises includes 158 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 158 problems in chapter 7: Chapter 7 Review Exercises have been answered, more than 75235 students have viewed full stepbystep solutions from this chapter. Introductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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.

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!).

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Solvable system Ax = b.
The right side b is in the column space of A.

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.

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

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.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.