Using Matlab, implement Gaussian Elimination with Partial Pivoting based on

Algorithm $2\mathrm{.}4$ on p$.72$ in Heath. Make your implementation as efficient as possible. Write

a Matlab script which clearly demonstrates that your code works as intended. Turn$-$in your

Matlab code and outputWe note that the permutation matrix

$P=P_{n-1}cdots{P}_1$

permutes the rows of A into the order determined by partial pivoting. An alterna$-$

tive interpretation, therefore, is to think of partial pivoting as a way of determining

a row ordering for the system in which no interchanges would be required for nu$-$

merical stability $($though of course there is no way to determine such an ordering

in advance$).$ Thus, we obtain the factorization

$PA=LU,$

where now $L$ really is lower triangular. To solve the linear system $Ax=b,$ we

first solve the lower triangular system $Ly=Pb$ by forward$-$substitution, then the

upper triangular system $Ux=y$ by back$-$substitution.