 6.2.1: Fill in each blank so that the resulting statement is true.Using Ga...
 6.2.2: Fill in each blank so that the resulting statement is true.Using Ga...
 6.2.3: Fill in each blank so that the resulting statement is true.Using Ga...
 6.2.4: Fill in each blank so that the resulting statement is true.True or ...
 6.2.5: Fill in each blank so that the resulting statement is true.Using Ga...
 6.2.6: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.7: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.8: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.9: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.10: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.11: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.12: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.13: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.14: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.15: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.16: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.17: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.18: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.19: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.20: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.21: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.22: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.23: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.24: In Exercises 124, use Gaussian elimination to find the completesolu...
 6.2.25: In Exercises 2528, the first screen shows the augmentedmatrix,A, fo...
 6.2.26: In Exercises 2528, the first screen shows the augmentedmatrix,A, fo...
 6.2.27: In Exercises 2528, the first screen shows the augmentedmatrix,A, fo...
 6.2.28: In Exercises 2528, the first screen shows the augmentedmatrix,A, fo...
 6.2.29: The figure for Exercises 2932 shows the intersections of threeonew...
 6.2.30: The figure for Exercises 2932 shows the intersections of threeonew...
 6.2.31: The figure for Exercises 2932 shows the intersections of threeonew...
 6.2.32: The figure for Exercises 2932 shows the intersections of threeonew...
 6.2.33: The figure shows the intersections of four oneway streets.a. Set u...
 6.2.34: The vitamin content per ounce for three foods is given in thefollow...
 6.2.35: Three foods have the following nutritional content per ounce.a. A d...
 6.2.36: A company that manufactures products A, B, and C doesboth manufactu...
 6.2.37: Describe what happens when Gaussian elimination is used tosolve an ...
 6.2.38: Describe what happens when Gaussian elimination is used tosolve a s...
 6.2.39: In solving a system of dependent equations in three variables,one s...
 6.2.40: a. The figure shows the intersections of a number of onewaystreets...
 6.2.41: In Exercises 4144, determine whether eachstatement makes sense or d...
 6.2.42: In Exercises 4144, determine whether eachstatement makes sense or d...
 6.2.43: In Exercises 4144, determine whether eachstatement makes sense or d...
 6.2.44: In Exercises 4144, determine whether eachstatement makes sense or d...
 6.2.45: Consider the linear systemcx + 3y + z = a22x + 5y + 2az = 0x + y + ...
 6.2.46: Before beginning this exercise, the group needs to read andsolve Ex...
 6.2.47: You are choosing between two cellphone plans. Data Plan Aoffers a f...
 6.2.48: Find the inverse of f(x) = 3x  4. (Section 2.7, Example 2)
 6.2.49: A chemist needs to mix a 75% saltwater solution with a 50%saltwater...
 6.2.50: Exercises 5052 will help you prepare for the material covered inthe...
 6.2.51: Exercises 5052 will help you prepare for the material covered inthe...
 6.2.52: Exercises 5052 will help you prepare for the material covered inthe...
Solutions for Chapter 6.2: Inconsistent and Dependent Systems and Their Applications
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 6.2: Inconsistent and Dependent Systems and Their Applications
Get Full SolutionsChapter 6.2: Inconsistent and Dependent Systems and Their Applications includes 52 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780134469164. Since 52 problems in chapter 6.2: Inconsistent and Dependent Systems and Their Applications have been answered, more than 29818 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 7.

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).

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

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

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

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.

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

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).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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.

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.