Find the inverse of the matrix (if it exists)A=⎣⎡100220345⎦⎤

Question

Find the inverse of the matrix (if it exists)A=⎣⎡​100​220​345​⎦⎤​

Filo · Accepted Answer

A=⎣⎡​100​220​345​⎦⎤​Here, ∣A∣=1(10−0)=10  (expanding along the first column)Since, ∣A∣=0Hence, A−1 exists.We know that, adjA=CTSo, we will find out co-factors of each element of A.C11​=(−1)1+1∣∣​20​45​∣∣​⇒C11​=10C12​=(−1)1+2∣∣​00​45​∣∣​⇒C12​=0C13​=(−1)1+3∣∣​00​20​∣∣​⇒C13​=0C21​=(−1)2+1∣∣​20​35​∣∣​⇒C21​=−(10−0)=−10C22​=(−1)2+2∣∣​10​35​∣∣​⇒C22​=5−0=5C23​=(−1)2+3∣∣​10​20​∣∣​⇒C23​=0C31​=(−1)3+1∣∣​22​34​∣∣​⇒C31​=8−6=2C32​=(−1)3+2∣∣​10​34​∣∣​⇒C32​=−(4−0)=−4C33​=(−1)3+3∣∣​10​22​∣∣​⇒C33​=2−0=2So, the cofactor matrix C=⎣⎡​10−102​05−4​002​⎦⎤​⇒adjA= CT=⎣⎡​1000​−1050​2−42​⎦⎤​⇒A−1=∣A∣adjA​=101​⎣⎡​1000​−1050​2−42​⎦⎤​⇒A−1=⎣⎡​100​−121​ 0​51​ 5−2​ 51​ ​⎦⎤​

Question Text	Find the inverse of the matrix (if it exists) $A = ⎣ ⎡ 100220345 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the inverse of the matrix (if it exists)
$A = ⎣ ⎡ 100220345 ⎦ ⎤$

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Find the inverse of the matrix (if it exists)A=⎣⎡​100​220​345​⎦⎤​

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Find the inverse of the matrix (if it exists)
$A = ⎣ ⎡ 100220345 ⎦ ⎤$