 6.1: In Exercises 15, use matrices to find the complete solution toeach ...
 6.2: In Exercises 15, use matrices to find the complete solution toeach ...
 6.3: In Exercises 15, use matrices to find the complete solution toeach ...
 6.4: In Exercises 15, use matrices to find the complete solution toeach ...
 6.5: In Exercises 15, use matrices to find the complete solution toeach ...
 6.6: In Exercises 610, perform the indicated matrix operationsor solve t...
 6.7: In Exercises 610, perform the indicated matrix operationsor solve t...
 6.8: In Exercises 610, perform the indicated matrix operationsor solve t...
 6.9: In Exercises 610, perform the indicated matrix operationsor solve t...
 6.10: In Exercises 610, perform the indicated matrix operationsor solve t...
 6.11: In Exercises 811, use Gaussian elimination to find the completesolu...
 6.12: The figure shows the intersections of three oneway streets.The num...
 6.13: Find values for x, y, and z so that the following matrices areequal...
 6.14: In Exercises 1427, perform the indicated matrix operations giventha...
 6.15: In Exercises 1427, perform the indicated matrix operations giventha...
 6.16: In Exercises 1427, perform the indicated matrix operations giventha...
 6.17: In Exercises 1427, perform the indicated matrix operations giventha...
 6.18: In Exercises 1427, perform the indicated matrix operations giventha...
 6.19: In Exercises 1427, perform the indicated matrix operations giventha...
 6.20: In Exercises 1427, perform the indicated matrix operations giventha...
 6.21: In Exercises 1427, perform the indicated matrix operations giventha...
 6.22: In Exercises 1427, perform the indicated matrix operations giventha...
 6.23: In Exercises 1427, perform the indicated matrix operations giventha...
 6.24: In Exercises 1427, perform the indicated matrix operations giventha...
 6.25: In Exercises 1427, perform the indicated matrix operations giventha...
 6.26: In Exercises 1427, perform the indicated matrix operations giventha...
 6.27: In Exercises 1427, perform the indicated matrix operations giventha...
 6.28: Solve for X in the matrix equation3X + A = B, where A = c 4 65 0d ...
 6.29: In Exercises 2930, use nine pixels in a 3 * 3 grid and the colorlev...
 6.30: In Exercises 2930, use nine pixels in a 3 * 3 grid and the colorlev...
 6.31: The figure shows a right triangle in a rectangular coordinate syste...
 6.32: The figure shows a right triangle in a rectangular coordinate syste...
 6.33: The figure shows a right triangle in a rectangular coordinate syste...
 6.34: The figure shows a right triangle in a rectangular coordinate syste...
 6.35: The figure shows a right triangle in a rectangular coordinate syste...
 6.36: The figure shows a right triangle in a rectangular coordinate syste...
 6.37: In Exercises 3738, find the products AB and BA to determinewhether ...
 6.38: In Exercises 3738, find the products AB and BA to determinewhether ...
 6.39: In Exercises 3942, find A1. Check that AA1 = I and A1A = I.A = c...
 6.40: In Exercises 3942, find A1. Check that AA1 = I and A1A = I.A = c...
 6.41: In Exercises 3942, find A1. Check that AA1 = I and A1A = I.A = C...
 6.42: In Exercises 3942, find A1. Check that AA1 = I and A1A = I.A = C...
 6.43: In Exercises 4344,a. Write each linear system as a matrix equation ...
 6.44: In Exercises 4344,a. Write each linear system as a matrix equation ...
 6.45: Use the coding matrix A = c3 24 3d and its inverseA1 = c 3 24 3d...
 6.46: In Exercises 4651, evaluate each determinant2 3 21 52
 6.47: In Exercises 4651, evaluate each determinant22 34 82
 6.48: In Exercises 4651, evaluate each determinant32 4 31 1 52 4 03
 6.49: In Exercises 4651, evaluate each determinant34 7 05 6 03 2 4
 6.50: In Exercises 4651, evaluate each determinant41 1 0 20 3 2 10 2 4 0...
 6.51: In Exercises 4651, evaluate each determinant2 2 2 20 2 2 20 0 2 20 ...
 6.52: In Exercises 5255, use Cramers Rule to solve each system.b x  2y =...
 6.53: In Exercises 5255, use Cramers Rule to solve each system.b7x + 2y =...
 6.54: In Exercises 5255, use Cramers Rule to solve each system.cx + 2y + ...
 6.55: In Exercises 5255, use Cramers Rule to solve each system.c2x + y = ...
Solutions for Chapter 6: Matrices and Determinants
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 6: Matrices and Determinants
Get Full SolutionsChapter 6: Matrices and Determinants includes 55 full stepbystep solutions. Since 55 problems in chapter 6: Matrices and Determinants have been answered, more than 29110 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780134469164. This textbook survival guide was created for the textbook: College Algebra , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

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.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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 ().

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.