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Let S be the set of all diagonal matrices.

To check if something is a subspace, my teacher gave us 3 conditions.

1.) 0 vector is in S

2) if U and V are in S, then U+V is in S

3) If V is in S and c is a scalar, then cV is in S.

I'm not really sure how to check the first condition. A guess no vectors on a diagnol 2x2 matrix can be the 0 vector,thus S is not a subspace in this case?