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Question: recall that a square matrix a is 1 symmetric if...

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Recall that a square matrix A is (1) symmetric if A^T = A, and (2) skew-symmetric if A^T = −A.

What are the dimensions of the following vector spaces? Justify your answers.

a) The space S, of all 3 × 3 symmetric matrices?

b) The space T , of all 3 × 3 skew-symmetric matrices?

c) The space S ∩ T ?

d) The space S + T ? What familiar vector space is this?

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