Find the inverse of the following matrix.⎣⎡250011−103⎦⎤

Question

Find the inverse of the following matrix.⎣⎡​250​011​−103​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​250​011​−103​⎦⎤​ ∣A∣=∣∣​250​011​−103​∣∣​=2(1(3)−0(1))−0+(−1)(5(1)−0(1))=6−5=1 Let Cij​ be the co-factor of an element in ith row and jth columnSo C11​=(−1)1+1∣∣​11​03​∣∣​=3C12​=(−1)1+2∣∣​50​03​∣∣​=−15C13​=(−1)1+3∣∣​50​11​∣∣​=5C21​=(−1)2+1∣∣​01​−13​∣∣​=−1C22​=(−1)2+2∣∣​20​−13​∣∣​=6C23​=(−1)2+3∣∣​20​01​∣∣​=−2C31​=(−1)3+1∣∣​01​−10​∣∣​=1C32​=(−1)3+2∣∣​25​−10​∣∣​=−5C33​=(−1)3+3∣∣​25​01​∣∣​=2Co-factor matrix C=⎣⎡​3−11​−156−5​5−22​⎦⎤​ adj(A)= CT=⎣⎡​3−155​−16−2​1−52​⎦⎤​ As we know thatA−1=∣A∣(adj(A))T​ =⎣⎡​3−155​−16−2​1−52​⎦⎤​

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

Find the inverse of the following matrix.
$⎣ ⎡ 250011 - 1 03 ⎦ ⎤$

Text solutionVerified

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Find the inverse of the following matrix.⎣⎡​250​011​−103​⎦⎤​

Text solutionVerified

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Find the inverse of the following matrix.
$⎣ ⎡ 250011 - 1 03 ⎦ ⎤$