A) let x be the set of all 3 x 3 matrices whose diagonal entries are all o. with the usual matrix addition and scalar multiplication, is x a vector space? (b) let y be the set of all 3 x 3 matrices whose diagonal entries add up to 0. with the usual matrix addition and scalar multipli- cation, is y a vector space? (e) let z be the set of all polynomials of degree exactly 5. is z a vector space?
(d) let v be the set of all 3 x 3 matrices whose determinant is equal to 0. with the usual matrix addition and scalar multiplication, is v a vector space? (e) let w be the vector space of all lower triangular 4 x 4 matrices what is the dimension of w?