Transform [ rrr 1 & -1 & 2 2 & 1 & 3 3 & 2 & 4 ] int into an uppe… - Vidyadip

Question

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

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Answer

Let $A=\left[\begin{array}{rrr}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]$

By $R_2-2 R_1$ and $R_3-3 R_1$, we get

$A \sim\left[\begin{array}{rrr}1 & -1 & 2 \\0 & 3 & -1 \\0 & 5 & -2\end{array}\right]$

By $R_3-\left(\frac{5}{3}\right) R_2$, we get,

$A \sim\left(\begin{array}{rrr}1 & -1 & 2 \\0 & 3 & -1 \\0 & 0 & -\frac{1}{3}\end{array}\right)$

This is an upper triangular matrix.

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