I have my final coming just around the corner and I got this practice test. Any help would be great.

1. Define .

Is T a linear transformation? If not, explain why not and provide a counterexample. If so, what is the geometric interpretation of the kernel of T?

2. Diagonalize

(I got Eigenvalues 2 and 3 and Eigenvectors )

3. Given is linear and T(1,2) = (3,4) and T(3,4) = (1,2), then T(4,3) = ?

(I got (-8, -9))