Answer the following questions. Upload your solutions as a pdf. You must show all necessary work to arrive at your conclusion to receive full credit. 1. If A is the matrix of a linear transformation which rotates all vectors in R? through %, explain why A cannot have any real eigenvalues. Is there an angle such that rotation through this angle would have a real eigenvalue? What eigenvectors would be obtainable in this way? 2. LetT(z,y) : R? R? be the transformation of reflecting a vector across the line y = mz. 1. Is this a linear transformation? Justify your answer? 2. Write a T as a matrix transformation by writing it as a composition of the common transformations. 3. Let A be am X m matrix with eigenvector v and its associated eigenvalue A # 0. Compare the eigenvalues of A and A71. 4. Let A be an X m matrix with eigenvector v and its associated eigenvalue A # 0. Let is a nonzero constant, compare the eigenvalues of A and cA