Find the inverse matrix of the following matrix.⎣⎡1122−135−1−1⎦⎤

Question

Find the inverse matrix of the following matrix.⎣⎡​112​2−13​5−1−1​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​112​2−13​5−1−1​⎦⎤​Then, ∣A∣=∣∣​112​2−13​5−1−1​∣∣​1(1+3)−2(−1+2)+5(3+2)=4−2+25∣A∣=27=0So, A−1 exists.Cofactors of matrix A,F11​=+∣∣​−13​−1−1​∣∣​−4F12​=−∣∣​12​−1−1​∣∣​=−1F13​=+∣∣​12​−13​∣∣​=5F21​=∣∣​23​5−1​∣∣​=17F22​=+∣∣​12​5−1​∣∣​=−11F23​=−∣∣​12​23​∣∣​=1F31​=+∣∣​2−1​5−1​∣∣​=3F32​=−∣∣​11​5−1​∣∣​=6F33​=+∣∣​11​2−1​∣∣​=−3Matrix made from adjoint of matrix A,B=⎣⎡​4173​−1−116​51−3​⎦⎤​Now,ajd.A=BT=⎣⎡​4173​−1−116​51−3​⎦⎤​Tadj.A=⎣⎡​4−15​17−111​36−3​⎦⎤​∴A−1=∣A∣adj.A​Hence,A−1=271​⎣⎡​4−15​17−111​36−3​⎦⎤​

Question Text	Find the inverse matrix of the following matrix. $⎣ ⎡ 112 2 - 1 3 5 - 1 - 1 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the inverse matrix of the following matrix.
$⎣ ⎡ 112 2 - 1 3 5 - 1 - 1 ⎦ ⎤$

Text solutionVerified

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Find the inverse matrix of the following matrix.⎣⎡​112​2−13​5−1−1​⎦⎤​

Text solutionVerified

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Find the inverse matrix of the following matrix.
$⎣ ⎡ 112 2 - 1 3 5 - 1 - 1 ⎦ ⎤$