4. Consider the vector space M of 2 x 3 matrices. (a) Define the subset SC M S = -{(a = a b = c) €M | a,b,c,dER} a 0 b-c d-a 0 d-c i. Show that S is closed under addition ii. Show that S is closed under scalar multiplication iii. Determine if S is a subspace of M. If so, find a basis and the dimension of the subspace. If not, provide a reason why it fails to be a subspace. (b) Let P be a fixed (but unknown) 3 x 2 matrix. Define a new subset Tp C M Tp = {A E MAP = PA} i. Show that Tp is closed under addition ii. Show that Tp is closed under scalar multiplication iii. Determine if Tp is a subspace of M. If so, find a basis and the dimension of the subspace. If not, provide a reason why it fails to be a subspace.

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