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The reciprocal matrix of {bmatrix} 1 & 0 & 2 0 & 1 & -1 1 &

Question

The reciprocal matrix of $⎣ ⎡ 101012 2 - 1 1 ⎦ ⎤$ is

⎣ ⎡ - 3 - 1 1 - 4 12 2 - 1 - 1 ⎦ ⎤

⎣ ⎡ 31 - 1 4 - 1 - 2 - 2 11 ⎦ ⎤

⎣ ⎡ - 3 - 4 2 - 1 1 - 1 12 - 1 ⎦ ⎤

⎣ ⎡ 3 - 1 - 1 4 - 1 - 2 - 2 11 ⎦ ⎤

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The reciprocal matrix of

⎣ ⎡ 101012 2 - 1 1 ⎦ ⎤

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Text solutionVerified

Given matrix is

⎣ ⎡ 101012 2 - 1 1 ⎦ ⎤

∣ A ∣ = 1

cofactor matrix is

⎣ ⎡ 34 - 2 - 1 - 1 1 - 1 - 2 1 ⎦ ⎤

a d j A = ⎣ ⎡ 3 - 1 - 1 4 - 1 - 2 - 2 11 ⎦ ⎤

∴ A^{- 1} = ⎣ ⎡ 3 - 1 - 1 4 - 1 - 2 - 2 11 ⎦ ⎤

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