1. (4 points) Compute A3 when A = CDC-1. C = (6 D = /2 4 2. (6 points) The matrix A = -2 has the factored characteristic equation -12 7 3 . f(2) = -(2+ 2)2(2 + 3). Is A diagonalizable? Explain why or why not. 3. (8 points) Let A = 10 - 6 7 - 3 Find a diagonal matrix D and an invertible matrix C such that A = CDC-1. 4. (6 points) Let A be a 2 x 2 matrix with real valued entries that has the eigenvalue M1 = 2 - V3 i for the eigenvector (2 - 4). ). What is the other eigenvalue and its corresponding eigenvector? 5. (8 points) Given the rotation scaling matrix A = (-3V3 3 -3 -3V3 a. What is the angle of rotation counterclockwise from the x-axis multiplying by this matrix produces? b. What is the scaling factor produced by multiplying by the matrix? 6. (8 points) Let A = ( ). Find a rotation scaling matrix B and an invertible matrix C such that A = CBC-1