Page 80 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(a) Give an example in which .

(b) Fill in the blank to create a matrix identity that is valid for all choices of A and B.
_________ .

Let A and B be square matrices with the same size. .
32.

(a) Give an example in which

(b) Let A and B be square matrices with the same size. Fill in the blank to create a matrix

identity that is valid for all choices of A and B. _________ .

In the real number system the equation has exactly two solutions. Find at least eight

33. different matrices that satisfy the equation .

Hint Look for solutions in which all entries off the main diagonal are zero.

A statement of the form “If p, then q” is logically equivalent to the statement “If not q, then not
34. p.” (The second statement is called the logical contrapositive of the first.) For example, the

logical contrapositive of the statement “If it is raining, then the ground is wet” is “If the ground

is not wet, then it is not raining.”

(a) Find the logical contrapositive of the following statement: If is singular, then A is
singular.

(b) Is the statement true or false? Explain.

Let A and B be matrices. Indicate whether the statement is always true or sometimes false.
35. Justify each answer.

(a)
(b)
(c)