Question: What is the difference between injective and surjective? How would you approach this question? 12. Define the following linear transformation T by: T : P3

What is the difference between injective and surjective? How would you approach this question?

12. Define the following linear transformation T by: T : P3 + R do + al + a2 + a3 p (t ) = ao + ant + ant? + agt3 a1 + a2 + a3 a2+ as a) Find the matrix for this transformation relative to the standard bases for each space (I.e. {1, t, 12, to } for P3 and e1, ez, es, e4 for IR4) b) Is T injective? Is T surjective? c) Find the matrix for this transformation relative to the bases {1, t, (2, (3} for PPs, and for IR4 d ) Find a polynomial that maps to , in other words, find a p(t) such that T(p(t) =

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