Using elementary transformations, find the inverse of the matrix $[\begin{matrix} 3 & 10 2 & 7 \end{matrix}]$

Open in App

Solution

$A = [\begin{matrix} 3 & 10 2 & 7 \end{matrix}]$

We know that $A = I A$ (using row operations)
$[\begin{matrix} 3 & 10 2 & 7 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] A$

Using operation $R_{1} \Rightarrow R_{1} - R_{2}$
$[\begin{matrix} 1 & 3 2 & 7 \end{matrix}] = [\begin{matrix} 1 & - 1 0 & 1 \end{matrix}] A$

Using operation $R_{2} \Rightarrow R_{2} - 2 R_{1}$
$[\begin{matrix} 1 & 3 0 & 1 \end{matrix}] = [\begin{matrix} 1 & - 1 - 2 & 3 \end{matrix}] A$

Using operation $R_{1} \Rightarrow R_{1} - 3 R_{2}$
$[\begin{matrix} 1 & 0 0 & 1 \end{matrix}] = [\begin{matrix} 7 & - 10 - 2 & 3 \end{matrix}] A$

Therefore,
$A^{- 1} = [\begin{matrix} 7 & - 10 - 2 & 3 \end{matrix}]$

Suggest Corrections

Similar questions

Using elementary transformations, find the inverse of matrix $[\begin{matrix} 3 & 10 2 & 7 \end{matrix}]$ , if it exists.

A = [\begin{matrix} 1 & 3 2 & 7 \end{matrix}]

Using elementary transformations, find the inverse of the followng matrix.

$[\begin{matrix} 3 & 1 5 & 2 \end{matrix}]$

Using elementary transformations, find the inverse of matrix $[\begin{matrix} 2 & 5 1 & 3 \end{matrix}]$ , if it exists.

Using elementary transformations, find the inverse of matrix $[\begin{matrix} 3 & - 1 - 4 & 2 \end{matrix}]$ , if it exists.

Join BYJU'S Learning Program