 8.6.1: In 1 and 2, verify that the matrix B is the inverse of the matrix A.
 8.6.2: In 1 and 2, verify that the matrix B is the inverse of the matrix A.
 8.6.3: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.4: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.5: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.6: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.7: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.8: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.9: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.10: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.11: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.12: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.13: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.14: In 314, use Theorem 8.6.3 to determine whether the given matrix is ...
 8.6.15: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.16: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.17: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.18: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.19: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.20: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.21: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.22: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.23: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.24: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.25: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.26: In 15  26, use Theorem 8.6.4 to find the inverse of the given matr...
 8.6.27: In 27 and 28, use the given matrices to find (AB) 1 .
 8.6.28: In 27 and 28, use the given matrices to find (AB) 1 .
 8.6.29: If A1 a 4 3 3 2b , what is A?
 8.6.30: If A is nonsingular, then (AT ) 1 (A1 ) T . Verify this for A a 1 4...
 8.6.31: Find a value of x such that the matrix A a 4 3 x 4 b is its own inv...
 8.6.32: Find the inverse of A a sinu cosu cosu sinu b .
 8.6.33: A nonsingular matrix A is said to be orthogonal if A1 AT . (a) Veri...
 8.6.34: Show that if A is an orthogonal matrix (see 33), then det A 1.
 8.6.35: Suppose A and B are nonsingular n 3 n matrices. Then show that AB i...
 8.6.36: Suppose A and B are n 3 n matrices and that either A or B is singul...
 8.6.37: Suppose A is a nonsingular matrix. Then show that det A1 1>det A.
 8.6.38: Suppose A2 A. Then show that either A I or A is singular
 8.6.39: Suppose A and B are n 3 n matrices, A is nonsingular, and AB 0. The...
 8.6.40: Suppose A and B are n 3 n matrices, A is nonsingular, and AB AC. Th...
 8.6.41: Suppose A and B are nonsingular n 3 n matrices. Is A B necessarily ...
 8.6.42: Suppose A is a nonsingular matrix. Then show that AT is nonsingular.
 8.6.43: Suppose A and B are n 3 n nonzero matrices and AB 0. Then show that...
 8.6.44: Consider the 3 3 diagonal matrix A a11 0 0 0 a22 0 0 0 a33 . Determ...
 8.6.45: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.46: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.47: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.48: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.49: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.50: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.51: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.52: In 45  52, use an inverse matrix to solve the given system of equa...
 8.6.53: In 53 and 54, write the system in the form AX B. Use X A1 B to solv...
 8.6.54: In 53 and 54, write the system in the form AX B. Use X A1 B to solv...
 8.6.55: In 5558, without solving, determine whether the given homogeneous s...
 8.6.56: In 5558, without solving, determine whether the given homogeneous s...
 8.6.57: In 5558, without solving, determine whether the given homogeneous s...
 8.6.58: In 5558, without solving, determine whether the given homogeneous s...
 8.6.59: The system of equations for the currents i1, i2, and i3 in the netw...
 8.6.60: Consider the square plate shown in FIGURE 8.6.2, with the temperatu...
Solutions for Chapter 8.6: Inverse of a Matrix
Full solutions for Advanced Engineering Mathematics  6th Edition
ISBN: 9781284105902
Solutions for Chapter 8.6: Inverse of a Matrix
Get Full SolutionsSince 60 problems in chapter 8.6: Inverse of a Matrix have been answered, more than 23648 students have viewed full stepbystep solutions from this chapter. Chapter 8.6: Inverse of a Matrix includes 60 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 6. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781284105902.

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).

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

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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

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.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

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).

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

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Solvable system Ax = b.
The right side b is in the column space of A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

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

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.