a. Let W be the subspace of a 3X3 matrix, consisting precisely of all diagonal martices. Find, with proof a basis for W.

b. What is the dimension of the subspace of nxn matrix consisting precisely of all diagonal matrices? Justify your answer

c. Let W be the subspace of 3X3 matrix consisting precisely of all symmetric matrices. Find with proof a basis for W.

d. What is the dimension of the subspace of nxn matrix consisting precisely of all symmetric matrices? Justify your answer