This is a LONG-ANSWER QUESTION. Write all your work in full, showing all your steps, and submit a copy of your full solution in the submission dropbox area immediately after you finish the test. This written work will be graded out of 7. Let T be the linear transformation from R2 to R3 which is the composition of the following three transformations (in order): • S₁ R2 R2 dilates a vector by a factor of 2; S2 R2R2 rotates vectors by an angle of; S3 R2 R3 does the following: S3 (x, y) = (x + y, xy, x). : (a) Find the standard matrix for the linear transformation T. (b) Find the image of the vector v = (1,2). (c) Is T one-to-one? Explain why or why not. I will submit my work! Next