MATLAB

1.Generate a random 4 × 3 matrix A (with integer entries), by typing A = floor(10*rand(4,3)) Let E1, E2 and E3 be the elementary matrices generated in Example 1. Compute the products E1*A, E2*A and E3*A and compare A with each of the products. Describe the effect of each multiplication on the matrix A. What general pattern do you see? That is, what effect does multiplying a matrix A on the left by an elementary matrix have on the matrix A?

2.Let E be the permutation matrix defined in (L3.2).

Generate a 5 × 5 matrix A with integer entries using the command A = floor(10*rand(5))

(a) Compute the product EA and compare the answer with the matrix A. How are the two matrices related? Describe the effect on A of left multiplication by the permutation matrix E. Compute the product AE and compare the answer with the matrix A. How are the two matrices related? Describe the effect on A of right multiplication by the permutation matrix E.

(b) Compute E−1 and ET , and observe that they are also permutation matrices. What else do you observe about E−1 and ET ?