Find the inverse of the matrices , if it exists.⎣⎡1−32305−2−50⎦⎤

Question

Find the inverse of the matrices , if it exists.⎣⎡​1−32​305​−2−50​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​1−32​305​−2−50​⎦⎤​ We know that A=IA∴⎣⎡​1−32​305​−2−50​⎦⎤​=⎣⎡​100​010​001​⎦⎤​AApplying R2​→R2​+3R1​ and R3​→R3​−2R1​, we have:⎣⎡​100​39−1​−2−114​⎦⎤​=⎣⎡​13−2​010​001​⎦⎤​AApplying R1​→R1​+3R3​ and R2​→R2​+8R3​, We have:⎣⎡​100​01−1​10214​⎦⎤​=⎣⎡​−5−13−2​010​381​⎦⎤​AApplying R3​→R3​+R2​ , we have:⎣⎡​100​010​102125​⎦⎤​=⎣⎡​−5−13−15​011​389​⎦⎤​AApplying R3​→251​R3​, we have:⎣⎡​100​010​10211​⎦⎤​=⎣⎡​−5−13−53​ ​01251​ ​38259​ ​⎦⎤​AApplying R1​→R1​−10R3​ and R2​→R2​−21R3​, we have:⎣⎡​100​010​001​⎦⎤​=⎣⎡​1−52​ −53​ ​−52​ 254​ 251​ ​−53​ 2511​ 259​ ​⎦⎤​A∴A−1=⎣⎡​1−52​ −53​ ​−52​ 254​ 251​ ​−53​ 2511​ 259​ ​⎦⎤​

Question Text	Find the inverse of the matrices , if it exists. $⎣ ⎡ 1 - 3 2 305 - 2 - 5 0 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the inverse of the matrices , if it exists.
$⎣ ⎡ 1 - 3 2 305 - 2 - 5 0 ⎦ ⎤$

Text solutionVerified

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Find the inverse of the matrices , if it exists.⎣⎡​1−32​305​−2−50​⎦⎤​

Text solutionVerified

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Find the inverse of the matrices , if it exists.
$⎣ ⎡ 1 - 3 2 305 - 2 - 5 0 ⎦ ⎤$