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  3. let l r3 rightarrow p2 be a linear function...

Question: let l r3 rightarrow p2 be a linear function...

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Question 12. Let L R3 P2 be a linear function. Prove that Lis injective if and only if the following two sets are equal Note, in the first occurrence in the previous equation, 0 is the zero polynomial, that is the function, 2:R R, such that 2() 30 for all t E R. It is, of course, also the polynomial whose coefficients are all zero. Here are some steps: 1. recognize that this is of the form A B, and so you must provide a separate proof for each of A B and B A. 2. it could be helpful to try to do an argument by contrapositive to establish that A Bis true. 3. when working on B A, suppose you are investigating the possibility that x, y E R3 and L(x) L(y). What does the fact that L is linear say about L (x) L(y)?
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