Page 116 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) Show that is symmetric.

(b) Show that is symmetric.

Let A be an symmetric matrix.
16.

(a) Show that is symmetric if k is any nonnegative integer.

(b) If is a polynomial, is necessarily symmetric? Explain.

Let A be an upper triangular matrix, and let be a polynomial. Is necessarily upper triangular? Explain.
17.

Prove: If , then A is symmetric and .
18.

Find all 3 ×3 diagonal matrices A that satisfy .
19.

Let be an matrix. Determine whether A is symmetric.
20.

(a)

(b)

(c)

(d)

On the basis of your experience with 20, devise a general test that can be applied to a formula for to determine whether
21. is symmetric.

A square matrix A is called skew-symmetric if . Prove:
22.

(a) If A is an invertible skew-symmetric matrix, then is skew-symmetric.