Page 787 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

In each part, use the formula in Theorem 1.4.5 to compute the inverse of the matrix, and check your result by showing

35. that .

(a)

(b)

Let be a polynomial for which the coefficients , , , …, are real. Prove
36. that if z is a solution of the equation , then so is .

Prove: For any complex number z, and .
37.

Prove that
38.

Hint Let and use the fact that .

In each part, use the method of Example 4 in Section 1.5 to find , and check your result by showing that
39. .

(a)

(b)

Show that . Discuss the geometric interpretation of the result.
40.