As we have noted, a computer does not perform exact floating point arithmetic, and errors occur. Norms play a role in determining if one can depend on the solution to a linear system obtained using...

As we have noted, a computer does not perform exact floating point arithmetic, and errors occur. Norms play a role in determining if one can depend on the solution to a linear system obtained using Gaussian elimination. Assume that the entries of matrix
 are precise. Let
 be the true solution to the system
 and that

_a
is the solution obtained using Gaussian elimination. If the product

_a
is not exact, then

_a

 For each matrix, let
 be a vector consisting of all ones. Find the MATLAB solution
 Then multiply b by 0.999 and solve the system again to obtain
 Compute

₂. What are your conclusions