Question

find the inverse of the matrix
( 1 2 1 )
( 3 0 1 )
( 0 2 1 )
using adjoint method.

Answer 1

Attachment

[ Kinda Mark as Brainliest ]

$\huge{♡}{\underline{\mathtt{\pink{|}\orange{|}{\red{A}\pink{n}\green{g}\blue{e}\pink{l}\purple{i}\orange{c}\red{-}\pink{B}\green{a}\blue{e}\purple{|}\pink{|}}}}}{♡}$

Answer 2

The inverse matrix is

$\bf{A}^{ - 1} = \left[\begin{array}{ccc} 1& 0& - 1 \\ \\ \frac{ 3 }{ 2}& - \frac{1}{2} & - 1\\ \\ - 3& 1& 3\end{array}\right]$

Given:

• $\left[\begin{array}{ccc}1&2&1\\3&0&1\\0&2&1\end{array}\right]$

To find:

• Find the inverse of matrix.

Solution:

Inverse of matrix A is ${A}^{ - 1} = \frac{Adj. A }{ |A| }$

Step 1:

Let matrix is A.

$A = \left[\begin{array}{ccc}1&2&1\\3&0&1\\0&2&1\end{array}\right]$

Find its determinant.

$|A| = \left | \begin{array}{ccc}1&2&1\\3&0&1\\0&2&1\end{array}\right |$

or

$|A| = 1(0 - 2) - 2(3 - 0) + 1(6 - 0)$

or

$|A| = - 2 - 6 +6$

or

$|A| = - 2$

Because,

Determinant ≠0, Thus, inverse of matrix A exists.

Step 2:

Find Adjoint matrix; for that first find minor matrix then Co-factor matrix and take transpose of it.

$M_{ij} = \left[\begin{array}{ccc} - 2&3&6\\0&1& 2\\2& - 2& - 6\end{array}\right]$

Find Co-factor matrix.

$\bf C_{ij}=(-1)^{i+j}M_{ij}$

So,

$C_{ij} = \left[\begin{array}{ccc} - 2& - 3&6\\0&1& - 2\\2& 2& - 6\end{array}\right]$

Take transpose of C to find Adjoint matrix.

$Adj.(A) = \left[\begin{array}{ccc} - 2& 0&2\\ - 3&1& 2\\6& - 2& - 6\end{array}\right]$

Step 3:

Find inverse of matrix A.

${A}^{ - 1} = \frac{Adj. A }{ |A| }$

or

${A}^{ - 1} = \frac{ - 1 }{ 2} \left[\begin{array}{ccc} - 2& 0&2\\ - 3&1& 2\\6& - 2& - 6\end{array}\right]$

or

${A}^{ - 1} = \frac{ 1 }{ 2} \left[\begin{array}{ccc} 2& 0& - 2\\ 3& - 1& - 2\\ - 6& 2& 6\end{array}\right]$

or

${A}^{ - 1} = \left[\begin{array}{ccc} 1& 0& - 1 \\ \\ \frac{ 3 }{ 2}& - \frac{1}{2} & - 1\\ \\ - 3& 1& 3\end{array}\right]$

Thus,

Inverse of matrix is

$\bf{A}^{ - 1} = \left[\begin{array}{ccc} 1& 0& - 1 \\ \\ \frac{ 3 }{ 2}& - \frac{1}{2} & - 1\\ \\ - 3& 1& 3\end{array}\right]$

_______________________

Learn more:

1) Find the inverse of the matrix ( if exists ) and state the reason if it doesn't exists.

[tex]\left[ \begin{array} {ccc}...

https://brainly.in/question/45794046

2) Find the adjoint and the inverse of the matrix \left[\begin{array}{ccc}cos\alpha&-sin\alpha\\sin\alpha&cos\alpha\end{arr...

https://brainly.in/question/7029406