 6.4.1: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.2: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.3: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.4: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.5: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.6: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.7: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.8: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.9: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.10: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.11: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.12: In Exercises 112, find lh~ produciJ AB and BA to d~t~rmin~ 'Whethe...
 6.4.13: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.14: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.15: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.16: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.17: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.18: In Exercises 1318, UM the fact thall{ A  c d , thm ,..  1 [ d ...
 6.4.19: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.20: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.21: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.22: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.23: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.24: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.25: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.26: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.27: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.28: In Exercises 1928, find K' by fomring (A lii and then !ISing rok' ...
 6.4.29: In Exercises 2932, write each linear syslem as a motri:r eqtwtion ...
 6.4.30: In Exercises 2932, write each linear syslem as a motri:r eqtwtion ...
 6.4.31: In Exercises 2932, write each linear syslem as a motri:r eqtwtion ...
 6.4.32: In Exercises 2932, write each linear syslem as a motri:r eqtwtion ...
 6.4.33: In Exercises 3336, write ead1 matrit equatiotJ as a system of line...
 6.4.34: In Exercises 3336, write ead1 matrit equatiotJ as a system of line...
 6.4.35: In Exercises 3336, write ead1 matrit equatiotJ as a system of line...
 6.4.36: In Exercises 3336, write ead1 matrit equatiotJ as a system of line...
 6.4.37: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.38: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.39: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.40: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.41: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.42: In Exercises 3742. a. \Vritt' eadr linear system as a matrix equat...
 6.4.43: In Exercises 4344, find A1 and check. A  e"' ,s.x
 6.4.44: In Exercises 4344, find A1 and check. A  e"'  e Z
 6.4.45: In Exercises 4546, if I is tire multiplitativt idemity mat,;x of o...
 6.4.46: In Exercises 4546, if I is tire multiplitativt idemity mat,;x of o...
 6.4.47: In Exercises 4748, find (ABr'. A1 Ir1 and Jr1 A 1 What do you ob...
 6.4.48: In Exercises 4748, find (ABr'. A1 Ir1 and Jr1 A 1 What do you ob...
 6.4.49: Prove lhc following slatemcnl: !(A  [~ ~ ~1 a # 0. b ,. 0. < ,. o....
 6.4.50: Prove the rotlowing statement: lfA  [: !}ndad  bc,.O. then A1  ...
 6.4.51: In Exercises 5152, use the coding matrix A  _3 I _ an 11s1m:~ntK ...
 6.4.52: In Exercises 5152, use the coding matrix A  _3 I _ an 11s1m:~ntK ...
 6.4.53: In Exercises 5354, use the cotUng nwtrix A  [ ~  ~ ~1 and its in...
 6.4.54: In Exercises 5354, use the cotUng nwtrix A  [ ~  ~ ~1 and its in...
 6.4.55: What is the multiplicative identity matrix?
 6.4.56: If you are given two matrices, A and B,explain how to determine if ...
 6.4.57: Explain why a matrix that does not have the same number of rows and...
 6.4.58: Explain how to find the multiplicative inverse for a 2 X 2 invertib...
 6.4.59: Explain how to find the multiplicative inverse for a 3 X 3 invertib...
 6.4.60: Explain how to write a linear system or three equations in three va...
 6.4.61: Explain how to solve the matrix equation AX  B.
 6.4.62: What is a cryptogram?
 6.4.63: It's January I. and you\e written down your major goal (or the yea...
 6.4.64: A year has passed since Exercise 63. (lime flies when you're solvin...
 6.4.65: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.66: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.67: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.68: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.69: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.70: In Exercises 6570, use a graphing utility to find the muWplicative...
 6.4.71: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.72: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.73: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.74: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.75: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.76: In Exercises 7176, write each system in the form AX  B. Then solv...
 6.4.77: In Exercises 7778, use a coding matrix A of your choice. Use a gra...
 6.4.78: In Exercises 7778, use a coding matrix A of your choice. Use a gra...
 6.4.79: In Exercises 7982. determine whethereadJ statement makes sense or ...
 6.4.80: In Exercises 7982. determine whethereadJ statement makes sense or ...
 6.4.81: In Exercises 7982. determine whethereadJ statement makes sense or ...
 6.4.82: In Exercises 7982. determine whethereadJ statement makes sense or ...
 6.4.83: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.84: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.85: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.86: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.87: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.88: In Exercises 8388, determine whether eacll statement is true or fo...
 6.4.89: Give an example or a 2 X 2 matrix that is its own inverse.
 6.4.90: If A  [; ~J find (K'r'
 6.4.91: Find values of a for which the following matrix is not invertible: ...
 6.4.92: Each person in Lhe group should work with one partner. Send a coded...
 6.4.93: Exercises 9395 will help you prepare for the material c.overed in ...
 6.4.94: Exercises 9395 will help you prepare for the material c.overed in ...
 6.4.95: Exercises 9395 will help you prepare for the material c.overed in ...
Solutions for Chapter 6.4: Multiplicative Inverses of Matrices and Matrix Equations
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 6.4: Multiplicative Inverses of Matrices and Matrix Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 95 problems in chapter 6.4: Multiplicative Inverses of Matrices and Matrix Equations have been answered, more than 36989 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780321782281. This textbook survival guide was created for the textbook: College Algebra , edition: 6. Chapter 6.4: Multiplicative Inverses of Matrices and Matrix Equations includes 95 full stepbystep solutions.

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.

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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 •

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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 .

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.

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.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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 •

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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.

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

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

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