(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1.Show that the set M of symetric matrices is closed under addition and scalar multiplication.

2.Show that the set W diagonal matrices is not closed under addition and scalar multiplication.

3.Show that the set W of matrices such that transpose(A) = -A is closed under scalar addition and multiplication.

3. The attempt at a solution

ok, for the first one, they have given me the solution but I don't understand why they did that:

Let A and B be in M. then transpose(A)=A and transpose(B)=B.

transpose(A+B)=transpose(A)+transpose(B)=A+B. therefore, M is closed under addition. why do they use matrix transposition?? I don't understand the proof

as for2and3, i have no idea what to do. I don't know how to do it "mathematically", if you can understand what I mean

thank you

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# Homework Help: Vector spaces

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