Question

find the inverse of each of the following matrices (if exists) by wing elementary transformations. [2 -1 1 -1 2 -1 1 -1 2].







​

Answer 1

Solution :- Given A=[

1

2

2

−1

]

Now we find A

−1

by elementary row transformation

so, we can write

A=I.A

[

1

2

2

−1

]=[

1

0

0

1

].A

R

2

→R

2

−2R

1

[

1

0

2

−5

]=[

1

−2

0

1

].A

R

1

→R

1

+

5

2

R

2

[

1

0

0

−5

]=[

5

1

−2

5

2

1

].A

R

2

→

−5

R

2

[

1

0

0

1

]=

⎣

⎢

⎢

⎡

5

1

5

2

5

2

5

−1

⎦

⎥

⎥

⎤

.A

this form is I=A

−1

.A So, A

−1

=

⎣

⎢

⎢

⎡

5

1

5

2

5

2

5

−1

⎦

⎥

⎥

⎤

mark as brainliest