Can someone please help me solve these?

1. (20 pts) Let T : P4 - 12x2 be the linear transformation such that (a) (2 pts) What is T(3x4 - x)? = 3 1 (x") - T(x) (b) (2 pts ) Write the matrix of T with respect to the ordered basis {x4, x3, x2, x, 1} for P4 and the standard basis . 18 8 8 8 for 12X2 This matrix (i.e. your answer) will be called A in the remaining parts (c) (5 pts) What is a basis for the null space of A? (d) (5 pts) What is a basis for the column space of A? (e) (3 pts) What is the kernel of T? (f) (3 pts) Suppose B is a 7 x 5 matrix with the same null space as A. What is the dimension of the column space of B? Justify or show work.ojection of x onto the 4. (20 pts) Let W be the subspace of Pa spanned by the set S = (p1, Pz/P3), where Instruct P2 (t) = 13 + +2 - 1, P3 ( t ) = 13 + t - 3 aharsh p1 (t ) = 12 - 3t, (ding, this cover page) an (a) (10 pts) Is S linearly independent? If so, call it a basis B for W. If it is not, reduce it to of your work for full credit e Table (for teacher tion find a basis B for W. Question Point 1 questions (b)) (5 pts) Determine whether or not the constant polynomial c(t) = 1 belongs to W. 2 core 20 (c) (5pts) For p(t) = 13 + 12 + 3t + 2, find the coordinate vector [p(t)]B relative to the basis 20 B that you found in Part (a). If it cannot be done, explain why. Total M O (RzGR, ) M Since pirot in every cal M linearly independent - 127 5 3 R TRg = RT 1 - 3 9 R3 + Rx= K3 So : (IPIl B ) + cope ( D+ (spilt ) score