Page 165 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let A and B be matrices. Show that if A is invertible, then .
16.

17.
(a) Express

as a sum of four determinants whose entries contain no sums.
(b) Express

as a sum of eight determinants whose entries contain no sums.

Prove that a square matrix A is invertible if and only if is invertible.
18.

Prove Cases 2 and 3 of Lemma Lemma 2.3.2.
19.

Let A and B be matrices. You know from earlier work that and need not be equal.

20. Is the same true for and ? Explain your reasoning.

Let A and B be matrices. You know from earlier work that is invertible if A and B are
21. invertible. What can you say about the invertibility of if one or both of the factors are

singular? Explain your reasoning.

Indicate whether the statement is always true or sometimes false. Justify each answer by giving
22. a logical argument or a counterexample.

(a)

(b)

(c) , then the homogeneous system has infinitely many solutions.
(d) If