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If A = {bmatrix} 2& -1 1 & 3{bmatrix}, then A^{-1} = ?

Question

If $A = [21 - 1 3]$ , then $A^{- 1} = ?$

⎣ ⎡ \frac{3}{7} \frac{1}{7} \frac{- 1}{7} \frac{2}{7} ⎦ ⎤

⎣ ⎡ \frac{3}{7} \frac{- 1}{7} \frac{1}{7} \frac{2}{7} ⎦ ⎤

⎣ ⎡ \frac{3}{7} \frac{1}{7} \frac{1}{7} \frac{2}{7} ⎦ ⎤

None of these

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Luna Discussed

A = [21 - 1 3]

, then

A^{- 1} = ?

8 mins ago

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8 mins ago

Text solutionVerified

∣ A ∣ = ∣ ∣ 21 - 1 3 ∣ ∣ = (6 + 1) = 7 \neq = 0

M_{11} = 3, M_{12} = 1, M_{21} = - 1

and

M_{22} = 2

∴ C_{11} = 3, C_{12} = - 1, C_{21} = 1

and

C_{22} = 2

\Rightarrow A d j A = [31 - 1 2]^{T} = [3 - 1 12]

\Rightarrow A^{- 1} = \frac{1}{∣ A ∣} (a d j A) = \frac{1}{7} [3 - 1 12] = ⎣ ⎡ \frac{3}{7} - \frac{1}{7} \frac{1}{7} \frac{2}{7} ⎦ ⎤

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