Let A be an 2 x 2 matrix such that the linear transformation T induced by A reects points in 1E2 across the xaxis and then multiplies the ycoordinate by some integer c greater than 1. a. 13. Find T931] and TIIEZ}. Find the eigenvalue(s3 of A. You must show every step of the mathematical work that supports your conclusion to receive credit. Find one eigenvector corresponding to each eigenvalue. You must show every step of the mathematical work that supports your conclusion to receive credit. Is there enough information given to determine whether A is diagonalizahle? If so, determine whether A is diagonaliaable or not and justify your response using complete sentences. If not, then explain why there is not enough information using complete sentences. Is there enough information given to determine the rank(A}? If so, determine the rankl) and justify your response using complete sentences. If not, then explain why there is not enough information using complete sentences. Is there enough information given to determine the dimension of the null space of A (i.e., dim [null[A]}? If so, determine the dim [null[A]} and justify your response using complete sentences. If not, then explain why there is not enough information using complete sentences. Is there enough information given to determine the dimension of the image of T (i.e., dim [ImlITj]? H'so, determine the dim [Im(T) and justify your response using complete sentences. If not, then explain why there is not enough information using complete sentences. Is there enough information given to determine whether A is invertible? If so= determine whether A is invertible or not and justify your response using complete sentences. If not, then explain why there is not enough information using complete sentences