4. (5 points) Let A and B ben x n matrices. Prove that if A and...

Question

Question

4. (5 points) Let A and B ben x n matrices. Prove that if A and B are skew symmetric, then A - B is skew symmetric. Recall C

math algebra

Answer 1

Answer #1

Since A and B are skew-symmetric matrices, then we have,

A^T = -A

B^T = -B

.

Now we have,

(A - B)^T

= A^T - B^T

= -A - (-B)

= -A + B

= -(A - B)

.

So, we have, (A - B)^T = -(A - B)

This implies that the matrix (A - B) is skew-symmetric.

Answer 2

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