Question

Transform $\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$ into an upper triangular matrix by suitable column transformations.

Answer 1

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

$=\left[\begin{array}{ccc}1& -1& 2\\ 0& 3& -1\\ 0& 0& -0.33\end{array}\right]$

$=\left[\begin{array}{ccc}3& 2& 4\\ 0& -1.67& 0.67\\ 0& 0& 0.20\end{array}\right]$

$=\left[\begin{array}{ccc}4& 2& 3\\ 0& -2& -0.5\\ 0& 0& -0.13\end{array}\right]$