 9.1: In Exercises 1 to 30, solve each system of equations.
 9.2: In Exercises 1 to 30, solve each system of equations.
 9.3: In Exercises 1 to 30, solve each system of equations.
 9.4: In Exercises 1 to 30, solve each system of equations.
 9.5: In Exercises 1 to 30, solve each system of equations.
 9.6: In Exercises 1 to 30, solve each system of equations.
 9.7: In Exercises 1 to 30, solve each system of equations.
 9.8: In Exercises 1 to 30, solve each system of equations.
 9.9: In Exercises 1 to 30, solve each system of equations.
 9.10: In Exercises 1 to 30, solve each system of equations.
 9.11: In Exercises 1 to 30, solve each system of equations.
 9.12: In Exercises 1 to 30, solve each system of equations.
 9.13: In Exercises 1 to 30, solve each system of equations.
 9.14: In Exercises 1 to 30, solve each system of equations.
 9.15: In Exercises 1 to 30, solve each system of equations.
 9.16: In Exercises 1 to 30, solve each system of equations.
 9.17: In Exercises 1 to 30, solve each system of equations.
 9.18: In Exercises 1 to 30, solve each system of equations.
 9.19: In Exercises 1 to 30, solve each system of equations.
 9.20: In Exercises 1 to 30, solve each system of equations.
 9.21: In Exercises 1 to 30, solve each system of equations.
 9.22: In Exercises 1 to 30, solve each system of equations.
 9.23: In Exercises 1 to 30, solve each system of equations.
 9.24: In Exercises 1 to 30, solve each system of equations.
 9.25: In Exercises 1 to 30, solve each system of equations.
 9.26: In Exercises 1 to 30, solve each system of equations.
 9.27: In Exercises 1 to 30, solve each system of equations.
 9.28: In Exercises 1 to 30, solve each system of equations.
 9.29: In Exercises 1 to 30, solve each system of equations.
 9.30: In Exercises 1 to 30, solve each system of equations.
 9.31: In Exercises 31 to 36, find the partial fraction decomposition.
 9.32: In Exercises 31 to 36, find the partial fraction decomposition.
 9.33: In Exercises 31 to 36, find the partial fraction decomposition.
 9.34: In Exercises 31 to 36, find the partial fraction decomposition.
 9.35: In Exercises 31 to 36, find the partial fraction decomposition.
 9.36: In Exercises 31 to 36, find the partial fraction decomposition.
 9.37: In Exercises 37 to 48, graph the solution set of each inequality.
 9.38: In Exercises 37 to 48, graph the solution set of each inequality.
 9.39: In Exercises 37 to 48, graph the solution set of each inequality.
 9.40: In Exercises 37 to 48, graph the solution set of each inequality.
 9.41: In Exercises 37 to 48, graph the solution set of each inequality.
 9.42: In Exercises 37 to 48, graph the solution set of each inequality.
 9.43: In Exercises 37 to 48, graph the solution set of each inequality.
 9.44: In Exercises 37 to 48, graph the solution set of each inequality.
 9.45: In Exercises 37 to 48, graph the solution set of each inequality.
 9.46: In Exercises 37 to 48, graph the solution set of each inequality.
 9.47: In Exercises 37 to 48, graph the solution set of each inequality.
 9.48: In Exercises 37 to 48, graph the solution set of each inequality.
 9.49: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.50: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.51: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.52: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.53: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.54: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.55: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.56: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.57: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.58: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.59: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.60: In Exercises 49 to 60, graph the solution set of each system of ine...
 9.61: In Exercises 61 to 65, solve the linear programming problem. In eac...
 9.62: In Exercises 61 to 65, solve the linear programming problem. In eac...
 9.63: In Exercises 61 to 65, solve the linear programming problem. In eac...
 9.64: In Exercises 61 to 65, solve the linear programming problem. In eac...
 9.65: In Exercises 61 to 65, solve the linear programming problem. In eac...
 9.66: Maximize Profit A manufacturer makes two types of golf clubs: a sta...
 9.67: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.68: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.69: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.70: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.71: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.72: In Exercises 67 to 73, solve each exercise by solving a system of e...
 9.73: In Exercises 67 to 73, solve each exercise by solving a system of e...
Solutions for Chapter 9: College Algebra and Trigonometry 7th Edition
Full solutions for College Algebra and Trigonometry  7th Edition
ISBN: 9781439048603
Solutions for Chapter 9
Get Full SolutionsCollege Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048603. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9 includes 73 full stepbystep solutions. Since 73 problems in chapter 9 have been answered, more than 5880 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra and Trigonometry, edition: 7.

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

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.

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

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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).

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.

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

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