Chapter 2.5, Problem 17E

When A is invertible, MATLAB finds A⁻¹ by factoring A = LU (where L may be permuted lower triangular), inverting L and U, and then computing U^−lL^−l. Use this method to compute the inverse of A in Exercise 2. (Apply the algorithm of Section 2.2 to L and to U.)

2. $A=\left[\begin{array}{ccc}4& 3& -5\\ -4& -5& 7\\ 8& 6& -8\end{array}\right],b=\left[\begin{array}{c}2\\ -4\\ 6\end{array}\right]$

$A=\left[\begin{array}{ccc}1& 0& 0\\ -1& 1& 0\\ 2& 0& 1\end{array}\right]\left[\begin{array}{ccc}4& 3& -5\\ 0& -2& 2\\ 0& 0& 2\end{array}\right]$