Question: Please explain and write neatly, so I can understand! DefineT : P3 > R3 by T09963 + bx2 + cx + d) = (21) +

Please explain and write neatly, so I can understand!

DefineT : P3 > R3 by T09963 + bx2 + cx + d) = (21) + d, 2a + 21) + d,a 2b 20). You may assume that T is a linear transformation. (You don't need to prove this.) (a) (4) Find the kernel of T and give a basis for ker(T). (b) (2) Is T one-to-one? Justify. (c) (2) What is the dimension of the image of T? (d) (2) Is T onto? Why or why not

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