Find the inverse of the matrix, if it exists.⎣⎡250011−103⎦⎤

Question

Find the inverse of the matrix, if it exists.⎣⎡​250​011​−103​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​250​011​−103​⎦⎤​ We know that A=IA∴⎣⎡​250​011​−103​⎦⎤​=⎣⎡​100​010​001​⎦⎤​AApplying R1​→21​R1​, we have:⎣⎡​150​011​−21​ 03​⎦⎤​=⎣⎡​21​ 00​010​001​⎦⎤​AApplying R2​→R2​−5R1​, we have:⎣⎡​100​011​−21​ 25​ 3​⎦⎤​=⎣⎡​21​ −25​ 0​010​001​⎦⎤​AApplying R3​→R3​−R2​, we have:⎣⎡​100​010​−21​ 25​ 21​ ​⎦⎤​=⎣⎡​21​ −25​ 25​ ​01−1​001​⎦⎤​AApplying R3​→2R3​, we have:⎣⎡​100​010​001​⎦⎤​=⎣⎡​3−155​−16−2​1−52​⎦⎤​A∴A−1=⎣⎡​3−155​−16−2​1−52​⎦⎤​

Question Text	Find the inverse of the matrix, if it exists. $⎣ ⎡ 250011 - 1 03 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the inverse of the matrix, if it exists.
$⎣ ⎡ 250011 - 1 03 ⎦ ⎤$

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Find the inverse of the matrix, if it exists.⎣⎡​250​011​−103​⎦⎤​

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Find the inverse of the matrix, if it exists.
$⎣ ⎡ 250011 - 1 03 ⎦ ⎤$