1. Given the matrices A, B and C, compute:
(a) AC + BC (It is much faster if you use the distributive law for matrices first.)
(b) 2A - 3A
(c) Perform the Boolean Product operation on the following zero-one matrices.
Please refer to the attachment for the complete question.
Let A and B be arbitrary n x n matrices whose entries are real numbers.
(a) Use basic matrix laws only to expand (A + B)^2. Explain all steps.
(b) Is (A - B)(A + B) = A^2 - B^2 ? Explain as you did in part (a).
Please refer to the attachment for detailed answers.
Using distributive law for matrices, we can rewrite "AC + BC" as "(A + B)C". This will reduce two matrix multiplication and one matrix addition operations to one matrix multiplication and one matrix addition operations.
(A + B)
= | 0 0 0 |
| 0 3 0 |
| 1 0 1 |
(A + B)C
= | 0 0 |
|-3 0 |
| 3 -1 |