Question

1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y,...

1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y, 5x + y).

(a) Represent T as a matrix with respect to the standard basis for R 2 .

(b) First, show that B = {(1, 1),(−2, 5)} is another basis for R 2 . Then, represent T as a matrix with respect to B.

(c) Using either (a) or (b), find the kernel of T.

(d) Is T an isomorphism? Justify your answer.

(e) Find T −1 , if it exists.

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