Solution:
For elementary row operation we have,
![\begin{array}{l} A=I A \\ \Rightarrow\left[\begin{array}{lll} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{array}\right]=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \mathrm{A} \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-31d768cf97657824ebff4b97c2343226_l3.png "Rendered by QuickLaTeX.com")
Applying 
![\Rightarrow\left[\begin{array}{lll} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 3 & 1 & 1 \end{array}\right]=\left[\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right] \mathrm{A}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e61eea81cb0e51ac82aa4cb6be207968_l3.png "Rendered by QuickLaTeX.com")
Applying 
![\Rightarrow\left[\begin{array}{ccc} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & -5 & -8 \end{array}\right]=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & -3 & 1 \end{array}\right] A](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3753ec328e737e430ec386df022e5b44_l3.png "Rendered by QuickLaTeX.com")
Applying 
![\Rightarrow\left[\begin{array}{ccc} 1 & 0 & -1 \\ 0 & 1 & 2 \\ 0 & 0 & 2 \end{array}\right]=\left[\begin{array}{ccc} -2 & 1 & 0 \\ 1 & 0 & 0 \\ 5 & -3 & 1 \end{array}\right] A](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-db1136ffc3ec06645d4460a393669671_l3.png "Rendered by QuickLaTeX.com")
Applying 
![\Rightarrow\left[\begin{array}{ccc} 1 & 0 & -1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{ccc} -2 & 1 & 0 \\ 1 & 0 & 0 \\ \frac{5}{2} & \frac{-3}{2} & \frac{1}{2} \end{array}\right] A](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b12ad8958fdabcde3e5590d1844a1e9d_l3.png "Rendered by QuickLaTeX.com")
Applying 
![\Rightarrow\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{ccc} \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & 1 \\ \frac{5}{2} & -\frac{3}{2} & \frac{1}{2} \end{array}\right] \mathrm{A}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-abf9a647ddce696a39e4c89a5d75d6b3_l3.png "Rendered by QuickLaTeX.com")
Therefore, as it is known that
So
![\Rightarrow^{-1}=\left[\begin{array}{ccc} \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & 1 \\ \frac{5}{2} & -\frac{3}{2} & \frac{1}{2} \end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ca6d4ce6d959cc83ae1a10ffda40f665_l3.png "Rendered by QuickLaTeX.com")
Find the inverse of the following matrices by using elementary row transformations: ![\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ddb84dea812933bfa363477c0747dfb6_l3.png "Rendered by QuickLaTeX.com")
Solution:
For elementary row operation we have,
Applying
Applying
Applying
Applying
Applying
Therefore, as it is known that
So
