The questions, I am attaching is related to General Vector Spaces. Advance thank you for whoever answer these question on the attachment files. I just need explanation on how to do them. Because they're going come up to my test and I need to know it please. Just answer D to i please.

6. (16 points) Suppose that 7 : P3 - P2 is some linear transformation. If this is all the information that you are given, fill in the blank with either "one-to-one" or "onto": T cannot be Now, suppose T is given by: I( p(x) ) = 3p'(x) - 2p"(x)(x+3)+p(-1)(3x2 +2x -7). Compute T(5x3 - 8x2 + 6x - 7). c. Show that T is indeed a linear transformation. d. Let B = {1, x, x2, x3} and B' = {1, x, x2}, the standard bases for P3 and p2, respectively. Find [T] B,B/- e. Check that your answer to (d ) is correct by re-computing (b) using your answer to (d). f. Find the rref of [T] B.B/. d) mood for g. Find a basis for ker(T), if possible. Is Tone-to-one? (brimoil h. Find a basis for range(7), if possible. Is Tonto? i. State the Dimension Theorem in general and verify that it is true for this linear S transformation. transformation