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Determine whether or not the transformation T is linear. If the transformation is linear, nd the associated representation matrix (with respect to...

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1. Determine whether or not the transformation T is linear. If the transformation is linear, find the associated
representation matrix (with respect to the standard basis). (a) (1 pt) T (j) = (3312)
(b) (1 pt) T (j) = (”339)

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2. Find the representation matrix (with respect to the standard basis) for each linear transformation. (a) (1 pt) Counter—clockwise rotation by 60 degrees around the origin. (b) (1 pt) Reflection over the line y : —:;:.

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3. For the next two parts (a) and (b), use the matrix A = (11 :2). (a) (2 pts) Find all the eigenvalues for A. (b) (2 ptS) Find an eigenvector for each of the eigenvalues from part (a).

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