If A=⎣⎡011101110⎦⎤, then find A−1

Question

If A=⎣⎡​011​101​110​⎦⎤​, then find A−1

Filo · Accepted Answer

Given, A=⎣⎡​011​101​110​⎦⎤​Then ∣A∣=∣∣​011​101​110​∣∣​=0(0−1)−1(0−1)+(1−0)=0+1+1∣A∣=2=0So, A−1 exist.On finding adjoint of AF11​=+∣∣​01​10​∣∣​=(0−1)=−1F12​=−∣∣​11​10​∣∣​=−(0−1)=1F13​=+∣∣​11​01​∣∣​=(1−0)=1F21​=−∣∣​11​10​∣∣​=−(0−1)=1F22​=+∣∣​01​10​∣∣​=(0−1)=−1F23​=−∣∣​01​11​∣∣​=−(0−1)=1F31​=+∣∣​10​11​∣∣​=(1−0)=1F32​=−∣∣​01​11​∣∣​=(0−1)=1F33​=+∣∣​01​10​∣∣​=(0−1)=−1B=⎣⎡​−111​1−11​11−1​⎦⎤​Adj.A=BT=⎣⎡​−111​1−11​11−1​⎦⎤​T=⎣⎡​−111​1−11​11−1​⎦⎤​∴A−1=∣A∣adj.A​So, A−1=21​⎣⎡​−111​1−11​11−1​⎦⎤​

Question Text	If $A = ⎣ ⎡ 011101110 ⎦ ⎤$ , then find $A^{- 1}$
Answer Type	Text solution:1
Upvotes	150

If $A = ⎣ ⎡ 011101110 ⎦ ⎤$ , then find $A^{- 1}$

Text solutionVerified

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If A=⎣⎡​011​101​110​⎦⎤​, then find A−1

Text solutionVerified

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If $A = ⎣ ⎡ 011101110 ⎦ ⎤$ , then find $A^{- 1}$