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A)Let X be the set of all 3x3 matrices whose diagonal entries are all 0. With the usual matrix addition and scalar multiplication, is X a vector
A)Let X be the set of all 3x3 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 x 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? d) Let V be the set of all 3x3 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 4x4 matrices. What is the dimension of W?
