Question

Consider the transformation, T : P1 → P2 defined by T(ax + b) = ax2 +...

Consider the transformation, T : P1 → P2 defined by T(ax + b) = ax2 + ax + a

(a) Find the image of 2x + 1.

(b) Find another element of P1 that has the same image.

(c) Is T a one-to-one transformation? Why or why not?

(d) Find ker(T) and determine the basis for ker(T). What is the dimension of kernel(T)?

(e) Find range(T) and determine a basis for range(T). What is the dimension of range(T)?

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