# Numerical Analysis/Inverse iteration exercises

Consider the matrix, ${\displaystyle A=\left[{\begin{array}{c c c}6&2&-1\\2&5&1\\-1&1&4\end{array}}\right]}$, and the vector, ${\displaystyle {\textbf {x}}^{(0)}=\left[{\begin{array}{c}1\\1\\1\\\end{array}}\right].}$
The LU decomposition of A is ${\displaystyle L=\left[{\begin{array}{c c c}1&0&0\\0.3333&1&0\\-0.167&0.3077&1\end{array}}\right],~~U=\left[{\begin{array}{c c c}6&2&-1\\0&4.333&1.333\\0&0&3.423\end{array}}\right]}$.
By hand, use the LU decomposition to do two iterations of the inverse power method (without shift) starting with ${\displaystyle {\textbf {x}}^{(0)}.}$