Question: 1. (10 pts) (a) Let T : R2 - R be a linear transformation that maps el = . [1]. and maps ez = [i]

1. (10 pts) (a) Let T : R2 - R be a linear transformation that maps el = . [1]. and maps ez = [i] into [ 3'] Use the fact that T is linear to find the image under T of |23 . (b) Determine, using any method, whether each of the following transformation is linear. Show details of your proof or arguments. (i) T(1, 22) = (21 - 42, 21 -5x2) (ii) T(21, 22) = (2x1 + 2, 3x1 - 422 + 6)2. (10 pts) (a) Let B = NOT OF and C= 1 3 Evaluate each of the matrix products, or say that it is undefined. (i) BC (ii)) CB (b) Let A = CT - CO . Find A, the transpose of A. Answers 1. 17 (6)(4) Yes (ii) No. For work, see Fall 2014 Exam 2, Problem 1. 5 0 2. (a) (i) 14 17 . (ii) Undefined. (b) AT = -3 1 5

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