Chapter 2.4, Problem 2E

Find the $\text{PA}=\text{LU}$ factorization (using partial pivoting) of the following matrices:

a. $\left[\begin{array}{ccc}1& 1& 0\\ 2& 1& -1\\ -1& 1& -1\end{array}\right]$

b. $\left[\begin{array}{ccc}0& 1& 3\\ 2& 1& 1\\ -1& -1& 2\end{array}\right]$

c. $\left[\begin{array}{ccc}1& 2& -3\\ 2& 4& 2\\ -1& 0& 3\end{array}\right]$

d. $\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 2\\ -2& 1& 0\end{array}\right]$