Question

find the adjoint and the inverse of the matrix A=1&2&\\3&-5\

Answer 1

A=  

⎝

⎜

⎜

⎛

​

 

1

2

3

​

 

2

3

1

​

 

3

1

2

​

 

⎠

⎟

⎟

⎞

​

 

∣A∣=1(6−1)−2(4−3)+3(2−6)

5−2−12

−9

Minor of A=  

⎝

⎜

⎜

⎛

​

 

5

1

−4

​

 

1

−4

−5

​

 

−4

−5

−1

​

 

⎠

⎟

⎟

⎞

​

 

Cof(A)=  

⎝

⎜

⎜

⎛

​

 

5

−1

−4

​

 

−1

−4

+5

​

 

−4

+5

−1

​

 

⎠

⎟

⎟

⎞

​

 

adj (A)=  

⎝

⎜

⎜

⎛

​

 

5

−1

−4

​

 

−1

−1

5

​

 

−4

5

−1

​

 

⎠

⎟

⎟

⎞

​

 

A  

−1

=  

∣A∣

adj(A)

​

=  

9

1

​

 

⎝

⎜

⎜

⎛

​

 

−5

1

4

​

 

1

4

−5

​

 

4

−5

1

​

 

⎠

⎟

⎟

⎞

​

 

=  

9

1

​

 

⎝

⎜

⎜

⎛

​

 

−5

−1

4

​

 

1

4

−5

​

 

4

−5

1

​

 

⎠

⎟

⎟

⎞

​

Answer 2

$\huge\mathfrak \red{Question}$

Find the inverse of matrix by adjoint method

$\tt{A = \: \left[\begin{array}{c c c}1 & 2 & 3 \\2 & 3 & 1 \\3 & 1 & 2\end{array}\right]}$

$\huge\mathfrak \pink{Answer}$

$\tt{A = \left(\begin{array}{c c c}1 & 2 & 3 \\2 & 3& 1 \\3& 1 & 2\end{array}\right)}$

$\tt{∣A∣=1(6−1)−2(4−3)+3(2−6)} \\\tt{5−2−12} \\\tt{−9}$

$\tt{Minor \: of \: A=\left(\begin{array}{c c c}5& 1& - 4 \\1 & - 4 & - 5\\- 4 & - 5& - 1\end{array}\right)}$

$\tt{Cof(A)= \left(\begin{array}{c c c}5& - 1& - 4 \\ - 1 & - 4 & + 5\\ - 4 & + 5& - 1\end{array}\right)}$

$\tt{adj (A)=\left(\begin{array}{c c c}5& - 1& - 4 \\ - 1 & - 1 & 5\\ - 4 & 5& - 1\end{array}\right)}$

$\tt{A^{-1} \: = \frac{adj(A)}{|A|} \: =\frac{1}{9}\left(\begin{array}{c c c} - 5& 1& 4 \\1 & 4 & - 5\\4 & - 5& 1\end{array}\right)}$

$\tt{= \frac{1}{9} \left(\begin{array}{c c c} - 5& 1& 4 \\ 1 & 4 & - 5\\ 4 & - 5& 1\end{array}\right)}$

I hope it's helps you ☺️.

Please markerd as brainliest answer ✌️✌️.