Define ????:????2 →????3 by ????(????(????))=(????(1),????(0),????(0)), where ????2 is the set of polynomials of degree at most 2.

(A) Determine whether ???? is a linear transformation or not.
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(B) Is ???? a matrix transformation? If yes, find its standard matrix. If not, explain why not.
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(C) Find the kernel of ????.
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(D) Find a basis and the dimension of the kernel of ????.
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(E) Find the range of ????.
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(F) Find a basis and the dimension of the range of ????.
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(G) Is ????(????)=1−????+????2 in the kernel of ?????
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(H) Find the coordinate vector of (5,4,4) relative to your ???? that you found in (F) above.
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