Find the inverse of the following matrix.⎣⎡013121231 ⎦⎤

Question

Find the inverse of the following matrix.⎣⎡​013​121​231 ​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​013​121​231 ​⎦⎤​ ∴∣A∣=⎣⎡​013​121​231 ​⎦⎤​ =0(2−3)−1(1−9)+2(1−6) =0+8−10 =−2=0 ∴A−1 exists.Consider AA−1=1 ∴ ⎣⎡​003​111​221​⎦⎤​A−1= ⎣⎡​010​100​001​⎦⎤​ By R1​↔R2​, we get,  ⎣⎡​103​211​321​⎦⎤​A−1= ⎣⎡​010​100​001​⎦⎤​ By R3​−3R1​, we get,  ⎣⎡​100​21−5​32−8​⎦⎤​A−1= ⎣⎡​010​10 −3​001​⎦⎤​By R1​−2R2​ and R3​+5R2​, we get, ⎣⎡​100​010​−122 ​⎦⎤​A−1= ⎣⎡​−215​10−3​001  ​⎦⎤​ By  \left  (\dfrac{1}{2}  \right  )R_{3}, we get,  ⎣⎡​100​010​−121​⎦⎤​A−1= ⎣⎡​−215/2​10−3/2​001/2​⎦⎤​ By R1​+R3​ an dR2​−2R3​, we get,  ⎣⎡​100​010​001​⎦⎤​A−1= ⎣⎡​1/2−45/2​−1/23 −3/2​1/2−11/2​⎦⎤​ ∴A−1=21​ ⎣⎡​1−85​−16−3​1−21 ​⎦⎤​

Question Text	Find the inverse of the following matrix. $⎣ ⎡ 013121231 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the inverse of the following matrix.
$⎣ ⎡ 013121231 ⎦ ⎤$

Text solutionVerified

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Find the inverse of the following matrix.⎣⎡​013​121​231 ​⎦⎤​

Text solutionVerified

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Find the inverse of the following matrix.
$⎣ ⎡ 013121231 ⎦ ⎤$