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If A = {bmatrix} -1 &-2 & -2 2& 1 & -2 2& -2 & 1 {bmatrix} the

Question

If A = $⎣ ⎡ - 1 22 - 2 1 - 2 - 2 - 2 1 ⎦ ⎤$ then Adj A =

A^{T}

2 A^{T}

3 A^{T}

4 A^{T}

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Elijah Discussed

If A =

⎣ ⎡ - 1 22 - 2 1 - 2 - 2 - 2 1 ⎦ ⎤

then Adj A =

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

A = ⎣ ⎡ - 1 22 - 2 1 - 2 - 2 - 2 1 ⎦ ⎤

A^{T} = ⎣ ⎡ - 1 - 2 - 2 21 - 2 2 - 2 1 ⎦ ⎤

Minor of

A = ⎣ ⎡ - 3 - 6 + 6 + 6 36 - 6 63 ⎦ ⎤

Co-factor

= ⎣ ⎡ - 3 - 6 + 6 + 6 36 - 6 63 ⎦ ⎤ ⎣ ⎡ + - + - + - + - + ⎦ ⎤

= ⎣ ⎡ - 3 + 6 + 6 - 6 3 - 6 - 6 - 6 3 ⎦ ⎤

= 3 ⎣ ⎡ - 1 + 2 + 2 - 2 1 - 2 - 2 - 2 1 ⎦ ⎤

Adj A

=

Transpose of co factor matrix

= 3 ⎣ ⎡ - 1 - 2 - 2 + 2 1 - 2 + 2 - 2 1 ⎦ ⎤

= 3 A^{T}

∴ A d j A = 3 A^{T}

Option C is correct answer

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