(1) (2 points) Let A, B denote m x n matrices. Explain why A = B iff Ax = Bx holds for all n-dimensional column vectors x in R". (2) (3 points) The vectors are a basis (which we HOW denote by B) for a subspace V C R4. Verify that the vector X = COX is in the subspace V, and compute the B-coordinates [x] 3. (3) (3 points) Let B denote the basis {v1, V2, v3} for RS defined by v1 = 2 N ,V2 (It is not necassary for you to check that this is a basis). There is a linear transformation T : R3 - R3 which satisfies T(vi) = ei for i=1,2,3. (Again, it is not necessary to check that this is true.) Find the standard matrix for T and find the B-matrix for T. (4) (2 points) Let T : R" - R" denote a linear transformation, and let A denote its standard matrix (this means T(x) = Ax for all n-dimensional column vectors x in R"). If B denotes the standard basis {e1, e2, ..., en} for R", then show that the B-matrix for T is equal to A the standard matrix for T