Question

Apply the given elementary transformation of the following matrix.
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

$R_2\to R_2-2R_1$
$R_3\to R_3-3R_1$
$\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$
$R_3\to R_3-\frac{5}{3}{R}_2$
$\left[\begin{array}{ccc}1& -1& 2\\ 0& 3& -1\\ 0& 5& -2\end{array}\right]$
$\left[\begin{array}{ccc}1& -1& 2\\ 0& 3& -1\\ 0& 0& \frac{17}{3}\end{array}\right]$
It is an upper triangular matrix.