 6.6.1: Solvex2  7x  30 = 0
 6.6.2: Solve1x + 32 2  41x + 32 + 3 = 0
 6.6.3: Approximate the solution(s) to x3 = x2  5 using a graphing utility
 6.6.4: Approximate the solution(s) to x3  2x + 2 = 0 using a graphing uti...
 6.6.5: In 532, solve each logarithmic equation. Express irrational solutio...
 6.6.6: In 532, solve each logarithmic equation. Express irrational solutio...
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 6.6.33: In 3360,solve each exponential equation. Express irrational solutio...
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 6.6.60: In 3360,solve each exponential equation. Express irrational solutio...
 6.6.61: In 6174, use a graphing utility to solve each equation. Express you...
 6.6.62: In 6174, use a graphing utility to solve each equation. Express you...
 6.6.63: In 6174, use a graphing utility to solve each equation. Express you...
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 6.6.74: In 6174, use a graphing utility to solve each equation. Express you...
 6.6.75: In 7586, solve each equation. Express irrational solutions in exact...
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 6.6.86: In 7586, solve each equation. Express irrational solutions in exact...
 6.6.87: 1f  g21x2 = 2. 1f + g21x2 = 7. f1x2 = g1x2. g1x2 = 4. f1x2 = 3. fa...
 6.6.88: 1f  g21x2 = 2. 1f + g21x2 = 3. f1x2 = g1x2. g1x2 = 3. f1x2 = 2. fa...
 6.6.89: a) If and graph f and g on the same Cartesian plane. (b) Find the p...
 6.6.90: a) If and graph f and g on the same Cartesian plane. (b) Find the p...
 6.6.91: (a) Graph and on the same Cartesian plane.(b) Shade the region boun...
 6.6.92: (a) Graph and on the same Cartesian plane. (b) Shade the region bou...
 6.6.93: a) Graph and on the same Cartesian plane. (b) Shade the region boun...
 6.6.94: (a) Graph and on the same Cartesian plane. (b) Shade the region bou...
 6.6.95: (a) Graph (b) Find the zero of f. (c) Based on the graph,solve
 6.6.96: (a) Graph (b) Find the zero of g. (c) Based on the graph,solve g1x2...
 6.6.97: A Population Model The resident population of the United States in ...
 6.6.98: A Population Model The population of the world in 2009 was 6.78 bil...
 6.6.99: Depreciation The value V of a Chevy Cobalt that is t years old can ...
 6.6.100: Depreciation The value V of a Honda Civic DX that is t years old ca...
 6.6.101: Fill in reasons for each step in the following two solutions. Solve...
Solutions for Chapter 6.6: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 6.6
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 6.6 includes 101 full stepbystep solutions. Since 101 problems in chapter 6.6 have been answered, more than 61063 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

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!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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

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 •

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

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.