 9.9.1.505: In Exercises 12, solve and graph the solution set on a number line....
 9.9.1.452: In Exercises 15, solve each linear inequality and graph the solutio...
 9.9.1.453: In Exercises 15, solve each linear inequality and graph the solutio...
 9.9.1.506: In Exercises 12, solve and graph the solution set on a number line....
 9.9.1.454: In Exercises 15, solve each linear inequality and graph the solutio...
 9.9.1.507: A company is planning to manufacture computer desks. The fixed cost...
 9.9.1.455: In Exercises 15, solve each linear inequality and graph the solutio...
 9.9.1.508: Find the intersection: {2, 4, 6, 8, 10} {4, 6, 12, 14}.
 9.9.1.509: Find the union: {2, 4, 6, 8, 10} {4, 6, 12, 14}.
 9.9.1.456: In Exercises 15, solve each linear inequality and graph the solutio...
 9.9.1.510: In Exercises 610, solve each compound inequality. Other than , grap...
 9.9.1.457: The cost and revenue functions for producing and selling x units of...
 9.9.1.511: In Exercises 610, solve each compound inequality. Other than , grap...
 9.9.1.458: Use this information to solve Exercises 710: A company is planning ...
 9.9.1.512: In Exercises 610, solve each compound inequality. Other than , grap...
 9.9.1.459: Use this information to solve Exercises 710: A company is planning ...
 9.9.1.513: In Exercises 610, solve each compound inequality. Other than , grap...
 9.9.1.460: Use this information to solve Exercises 710: A company is planning ...
 9.9.1.514: In Exercises 610, solve each compound inequality. Other than , grap...
 9.9.1.461: Use this information to solve Exercises 710: A company is planning ...
 9.9.1.515: In Exercises 1112, find the solution set for each equation. 5x 3 7
 9.9.1.462: A person can choose between two charges on a checking account. The ...
 9.9.1.463: A salesperson earns $500 per month plus a commission of 20% of sale...
 9.9.1.516: In Exercises 1112, find the solution set for each equation. 6x 1 4x 15
 9.9.1.464: In Exercises 1316, let A {a, b, c}, B {a, c, d, e}, and C {a, d, f,...
 9.9.1.517: In Exercises 1314, solve and graph the solution set on a number lin...
 9.9.1.465: In Exercises 1316, let A {a, b, c}, B {a, c, d, e}, and C {a, d, f,...
 9.9.1.518: In Exercises 1314, solve and graph the solution set on a number lin...
 9.9.1.466: In Exercises 1316, let A {a, b, c}, B {a, c, d, e}, and C {a, d, f,...
 9.9.1.519: The inequality b 98.6 8 describes a persons body temperature, b, in...
 9.9.1.467: In Exercises 1316, let A {a, b, c}, B {a, c, d, e}, and C {a, d, f,...
 9.9.1.520: In Exercises 1618, graph each inequality in a rectangular coordinat...
 9.9.1.468: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.521: In Exercises 1618, graph each inequality in a rectangular coordinat...
 9.9.1.469: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.522: In Exercises 1618, graph each inequality in a rectangular coordinat...
 9.9.1.470: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.523: In Exercises 1921, graph the solution set of each system of inequal...
 9.9.1.471: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.524: In Exercises 1921, graph the solution set of each system of inequal...
 9.9.1.472: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.525: In Exercises 1921, graph the solution set of each system of inequal...
 9.9.1.473: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.474: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.475: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.476: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.477: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.478: In Exercises 1727, solve each compound inequality. Other than , gra...
 9.9.1.479: To receive a B in a course, you must have an average of at least 80...
 9.9.1.480: In Exercises 2932, find the solution set for each equation. 2x 1 7
 9.9.1.481: In Exercises 2932, find the solution set for each equation. 3x 2 5
 9.9.1.482: In Exercises 2932, find the solution set for each equation. 2 x 3 7 10
 9.9.1.483: In Exercises 2932, find the solution set for each equation. 4x 3 7x 9
 9.9.1.484: In Exercises 3337, solve each absolute value inequality. Other than...
 9.9.1.485: In Exercises 3337, solve each absolute value inequality. Other than...
 9.9.1.486: In Exercises 3337, solve each absolute value inequality. Other than...
 9.9.1.487: In Exercises 3337, solve each absolute value inequality. Other than...
 9.9.1.488: In Exercises 3337, solve each absolute value inequality. Other than...
 9.9.1.489: Approximately 90% of the population sleeps h hours daily, where h i...
 9.9.1.490: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.491: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.492: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.493: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.494: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.495: In Exercises 3944, graph each inequality in a rectangular coordinat...
 9.9.1.496: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.497: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.498: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.499: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.500: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.501: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.502: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.503: In Exercises 4553, graph the solution set of each system of inequal...
 9.9.1.504: In Exercises 4553, graph the solution set of each system of inequal...
Solutions for Chapter 9: CHAPTER 9 REVIEW EXERCISES
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 9: CHAPTER 9 REVIEW EXERCISES
Get Full SolutionsChapter 9: CHAPTER 9 REVIEW EXERCISES includes 74 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 74 problems in chapter 9: CHAPTER 9 REVIEW EXERCISES have been answered, more than 90434 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. Introductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941.

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.

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

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

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).

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

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

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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

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 •

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.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.