Name: Finding Inverse by Elementary Transformations
Uploaded: 2019-07-19
Duration: 12 min 5 s
Description: In this video, we will learn to find the inverse of matrices using elementary transformations of matrices. We will learn how to find the inverse of a matrix,...

Question

Find the inverse of each of the following matrices.

$[\begin{array}{l} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{array}]$

Accepted Answer

Given that $[\begin{array}{l} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{array}]$

Now, $C_{11} = |\begin{array}{l} 3 & 1 \\ 1 & 2 \end{array}| = 5, C_{12} = - |\begin{array}{l} 2 & 1 \\ 3 & 2 \end{array}| = - 1$ and $C_{13} = |\begin{array}{l} 2 & 3 \\ 3 & 1 \end{array}| = - 7$

$C_{21} = - |\begin{array}{l} 2 & 3 \\ 1 & 2 \end{array}| = - 1, C_{22} = |\begin{array}{l} 1 & 3 \\ 3 & 2 \end{array}| = - 7$ and $C_{23} = - |\begin{matrix} 1 & 2 \\ 3 & 1 \end{matrix}| = 5$

$C_{31} = |\begin{matrix} 2 & 3 \\ 3 & 1 \end{matrix}| = - 7, C_{32} = - |\begin{matrix} 1 & 3 \\ 2 & 1 \end{matrix}| = 5$ and $C_{33} = |\begin{array}{l} 1 & 2 \\ 2 & 3 \end{array}| = - 1$

$adj A = {[\begin{matrix} 5 & - 1 & - 7 \\ - 1 & - 7 & 5 \\ - 7 & 5 & - 1 \end{matrix}]}^{⊤} = [\begin{matrix} 5 & - 1 & - 7 \\ - 1 & - 7 & 5 \\ - 7 & 5 & - 1 \end{matrix}]$

and $| A | = - 18$

we know that $A^{- 1} = \frac{1}{|A|} a d j A$

$∴ A^{- 1} = - \frac{1}{18} [\begin{matrix} 5 & - 1 & - 7 \\ - 1 & - 7 & 5 \\ - 7 & 5 & - 1 \end{matrix}]$

Find the inverse of each of the following matrices.

$[\begin{array}{l} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{array}]$

Important Questions on Adjoint and Inverse of a Matrix

Learn and Prepare for any exam you want !

Find the inverse of each of the following matrices. 123231312

Important Questions on Adjoint and Inverse of a Matrix

Learn and Prepare for any exam you want !

Find the inverse of each of the following matrices.

$[\begin{array}{l} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{array}]$