8. When we explored matrix multiplication in Section 2.2, we saw that some properties that are true for real numbers are not true for matrices. This exercise will investigate that in some more depth. a. Suppose that A and B are two matrices and that AB = 0. If B # 0, what can you say about the linear independence of the columns of A? b. Suppose that we have matrices A, B and C such that AB = AC. We have seen that we cannot generally conclude that B = C. If we assume additionally that A is a matrix whose columns are linearly independent, explain why B = C. You may wish to begin by rewriting the equation AB = AC as AB – AC = A(B – C) = 0.
8. When we explored matrix multiplication in Section 2.2, we saw that some properties that are true for real numbers are not true for matrices. This exercise will investigate that in some more depth. a. Suppose that A and B are two matrices and that AB = 0. If B # 0, what can you say about the linear independence of the columns of A? b. Suppose that we have matrices A, B and C such that AB = AC. We have seen that we cannot generally conclude that B = C. If we assume additionally that A is a matrix whose columns are linearly independent, explain why B = C. You may wish to begin by rewriting the equation AB = AC as AB – AC = A(B – C) = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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