Page 78 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let A, B, and 0 be matrices. Assuming that A is invertible, find a matrix C such that
18.

is the inverse of the partitioned matrix

(See Exercise 15 of the preceding section.)
Use the result in Exercise 18 to find the inverses of the following matrices.
19.

(a)

(b)

20. matrix A such that .
(a) Find a nonzero .

(b) Find a nonzero matrix A such that

A square matrix A is called symmetric if and skew-symmetric if . Show that if B is a square matrix, then
21.

(a) and are symmetric

(b) is skew-symmetric

If A is a square matrix and n is a positive integer, is it true that ? Justify your answer.
22.

Let A be the matrix
23.

Determine whether A is invertible, and if so, find its inverse.