Obtain the inverse of the following matrix using elementary operations:
$A = ⎣ ⎡ 013121231 ⎦ ⎤$

Question

Obtain the inverse of the following matrix using elementary operations:A=⎣⎡​0 1 3 ​121​231​⎦⎤​

Filo · Accepted Answer

We know thatAA−1=I∴ =⎣⎡​013​121​231​⎦⎤​A−1=⎣⎡​100​010​001​⎦⎤​R1​↔R2​,R3​→R3​−3R2​⎣⎡​100​21−5​32−8​⎦⎤​A−1 =⎣⎡​010​10−3​001​⎦⎤​R3​→R3​+5R2​,R1​→R1​−2R2​ ⎣⎡​100​010​−122​⎦⎤​A−1 =⎣⎡​−215​10−3​001​⎦⎤​R3​→21​R3​⎣⎡​100​010​−121​⎦⎤​A−1= ⎣⎡​−215/2​10−3/2​001/2​⎦⎤​R2​→R2​−2R3​,R1​→ R1​+R3​⎣⎡​100​010​001​⎦⎤​A−1=⎣⎡​1/2−45/2​−1/23−3/2​1/2−11/2​⎦⎤​∴IA−1=A−1=⎣⎡​1/2−45/2​−1/23−3/2​1/2−11/2​⎦⎤​

Question Text	Obtain the inverse of the following matrix using elementary operations: $A = ⎣ ⎡ 013121231 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Obtain the inverse of the following matrix using elementary operations:
$A = ⎣ ⎡ 013121231 ⎦ ⎤$

Text solutionVerified

Practice questions from similar books

Obtain the inverse of the following matrix using elementary operations:A=⎣⎡​0 1 3 ​121​231​⎦⎤​

Text solutionVerified

Practice questions from similar books

Obtain the inverse of the following matrix using elementary operations:
$A = ⎣ ⎡ 013121231 ⎦ ⎤$