Answer the following questions. You do not need to justify your answers. (a) Let X be the set of all 3×3 matrices whose diagonal entries are all 0. With the usual matrix addition and scalar multiplication, is X a vector space? (b) Let Y be the set of all 3 × 3 matrices whose diagonal entries add up to 0. With the usual matrix addition and scalar multiplication, is Y a vector space? (c) Let Z be the set of all polynomials of degree exactly 5. Is Z a vector space? Show all your work! continued on next page 1 2 DUE 11:00PM, FRIDAY, JUNE 5 (d) Let V be the set of all 3×3 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 4×4 matrices. What is the dimension of W?