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**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 for

**2**and

**3**, 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