Set A = floor(10 * rand(6)). By construction, the matrix A will have integer entries. Let us change the sixth column of A so as to make the matrix singular. Set
B = A', A(:,6) = -sum(B(l : 5, :))'
(a) Set x = ones(6, 1) and use MATLAB to compute Ax. Why do we know that A must be singular? Explain. Check that A is singular by computing its reduced row echelon form.
(b) Set
B = x * [1 : 6]
The product AB should equal the zero matrix. Why? Explain. Verify that this is so by computing AB using the MATLAB operation *.
(c) Set
C = floor(10 * rand(6)) and D = B + C
Although C ≠ D, the products AC and AD should be equal. Why? Explain. Compute A * C and A * D and verify that they are indeed equal.