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Q. Find A^-1 By using adjoint methodA= |
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Answer» We have, A=[ 2 4
−2 ] Now, COFACTOR of A a 11 =(−1) 1+1 ∣3∣ =3 a 12 =(−1) 1+2 ∣4∣ =−4 a 21 =(−1) 2+1 ∣−2∣ =2 a 22 =(−1) 2+2 ∣2∣ =2 ∴adj A=[ 3 2
−4 2 ] =[ 3 −4
2 2 ] Now, ∣A∣=[ 2 4
−2 3 ] =(2)(3)−(4)(−2) =6+8 =14 =0 A is non-singular. ∴A −1 EXISTS A −1 = ∣A∣ adj A
= 14 1 [ 3 −4
2 2 ] = ⎣ ⎢ ⎢ ⎡
14 3
− 14 4
14 2
14 2
⎦ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎡
14 3
− 7 2
7 1
7 1
⎦ ⎥ ⎥ ⎤
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