Chapter 2.2, Problem 2E

Find the LU factorization of the given matrices. Check by matrix multiplication.

$\text{a}.\left[\begin{array}{ccc}3& 1& 2\\ 6& 3& 4\\ 3& 1& 5\end{array}\right]$ $\text{b}.\left[\begin{array}{ccc}4& 2& 0\\ 4& 4& 2\\ 2& 2& 3\end{array}\right]$ $\text{c}.\left[\begin{array}{cccc}0& -1& 1& 2\\ 0& 2& 1& 0\\ 1& 3& 4& 4\\ 0& 2& 1& -1\end{array}\right]$