3
Question
Find the inverse of the given matrix
⎡⎢⎣1−1202−33−24⎤⎥⎦
Find the inverse of the given matrix
⎡⎢⎣1−1202−33−24⎤⎥⎦
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Solution
Let A=⎡⎢⎣1−1202−33−24⎤⎥⎦
We have, |A|=⎡⎢⎣1−1202−33−24⎤⎥⎦=1(8−6)−(−1)(0+9)+2(0−6)
=2+9−12=−1
Cofactors of A are
A11=8−6=2,A12=−(0=9)=−9,A13=0−6=−6,A21=(−4+4)=0,A22=4−6=−2,A23=−(−2+3)=−1A31=3−4=−1,A32=−(−3−0)=3,A33=2−0=2,
∴ adj(A)=⎡⎢⎣2−9−60−2−1−132⎤⎥⎦T=⎡⎢⎣20−1−9−23−6−12⎤⎥⎦
Now, A−1=1|A|(adj A)=1−1⎡⎢⎣20−1−9−23−6−12⎤⎥⎦=⎡⎢⎣−20192−361−2⎤⎥⎦
Let A=⎡⎢⎣1−1202−33−24⎤⎥⎦
We have, |A|=⎡⎢⎣1−1202−33−24⎤⎥⎦=1(8−6)−(−1)(0+9)+2(0−6)
=2+9−12=−1
Cofactors of A are
A11=8−6=2,A12=−(0=9)=−9,A13=0−6=−6,A21=(−4+4)=0,A22=4−6=−2,A23=−(−2+3)=−1A31=3−4=−1,A32=−(−3−0)=3,A33=2−0=2,
∴ adj(A)=⎡⎢⎣2−9−60−2−1−132⎤⎥⎦T=⎡⎢⎣20−1−9−23−6−12⎤⎥⎦
Now, A−1=1|A|(adj A)=1−1⎡⎢⎣20−1−9−23−6−12⎤⎥⎦=⎡⎢⎣−20192−361−2⎤⎥⎦
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