Question 1. (6 marks} ' For each of the following subsets in some vector spaces, determine whether it is a subspace. Explain why. If the subset is a subspace. nd a basis for the subspace and explain why the set you nd is a basis. a. H={(st,23,s+t) | sJER} C R3. b. Let M312 consist of all the 2 x 2 matrices. M'gxg with the matrix addition and scalar multiple operations forms a. vector space. Consider the subset U = {X E M2\" | AX + XA = O} with A = [:1 '11]. c. K={a:2+u+c|a:_>0.b,ces}c11=a. d. S:{pEP2Ip(l)=O}