Construct a matrix as follows. Set
B = eye(10) - triu(ones(10), 1)
Why do we know that B must be nonsingular? Set
C = inv(B) and x = C(:, 10)
Now change B slightly by setting B(10, 1) = -1/256. Use MATLAB to compute the product Bx. From the result of this computation, what can you conclude about the new matrix B? Is it still nonsingular? Explain. Use MATLAB to compute its reduced row echelon form.