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Find the inverse of matrix by adjoint method A=[ {matrix} 1 &

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Find the inverse of matrix by adjoint method
$A = ⎣ ⎡ 123231312 ⎦ ⎤$

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Find the inverse of matrix by adjoint method

A = ⎣ ⎡ 123231312 ⎦ ⎤

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Text solutionVerified

A = ⎝ ⎛ 123231312 ⎠ ⎞

∣ A ∣ = 1 (6 - 1) - 2 (4 - 3) + 3 (2 - 6)

5 - 2 - 12

- 9

Minor of A

= ⎝ ⎛ 51 - 4 1 - 4 - 5 - 4 - 5 - 1 ⎠ ⎞

C o f (A) = ⎝ ⎛ 5 - 1 - 4 - 1 - 4 + 5 - 4 + 5 - 1 ⎠ ⎞

adj (A)

= ⎝ ⎛ 5 - 1 - 4 - 1 - 1 5 - 4 5 - 1 ⎠ ⎞

A^{- 1} = \frac{a d j ( A )}{∣ A ∣} = \frac{1}{9} ⎝ ⎛ - 5 14 14 - 5 4 - 5 1 ⎠ ⎞

= \frac{1}{9} ⎝ ⎛ - 5 - 1 4 14 - 5 4 - 5 1 ⎠ ⎞

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Question Text	Find the inverse of matrix by adjoint method $A = ⎣ ⎡ 123231312 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150