Exercise. 15. Consider the matrix and an arbitrary 3 × 3 matrix E= -3 1 0 0 0 1 a C A = d e f 9 hk (a) Compute EA. Comment on the relationship between A and EA, in terms of the technique of elimination we learned. (b) Consider the matrix 0 00 0 1/4 0 01 and an arbitrary 3 x 3 matrix A. Compute EA. Comment on the relationship between A and EA. (c) Can you think of a 3 x 3 matrix such that EA is obtained from A by swapping the last two rows (for any 3 x 3 matrix A)? (d) The matrices of the forms introduced in parts (a), (b), and (c) are called elementary: An nxn matrix E is elementary if it can be obtained from I, by performing one of the three elementary row operations on In. Describe the format of the three types of elementary matrices.