Find the adjoint of matrix A=⎣⎡122130251⎦⎤

Question

Find the adjoint of matrix     A=⎣⎡​122​130​251​⎦⎤​

Filo · Accepted Answer

Let A=⎣⎡​122​130​251​⎦⎤​We know that adjA=CTSo, we will find out co-factors of each element of A.C11​=(−1)1+1∣∣​30​51​∣∣​⇒C11​=3−0=3C12​=(−1)1+2∣∣​22​51​∣∣​⇒C12​=−(2−10)=8C13​=(−1)1+3∣∣​22​30​∣∣​⇒C13​=0−6=−6C21​=(−1)2+1∣∣​10​21​∣∣​⇒C21​=−(1−0)=−1C22​=(−1)2+2∣∣​12​21​∣∣​⇒C22​=1−4=−3C23​=(−1)2+3∣∣​12​10​∣∣​⇒C23​=−(0−2)=2C31​=(−1)3+1∣∣​13​25​∣∣​⇒C31​=5−6=−1C32​=(−1)3+2∣∣​12​25​∣∣​⇒C32​=−(5−4)=−1C33​=(−1)3+3∣∣​12​13​∣∣​⇒C33​=3−2=1So, the cofactor matrix C=⎣⎡​3−1−1​8−3−1​−621​⎦⎤​⇒CT=⎣⎡​38−6​−1−32​−1−11​⎦⎤​Hence, adjA=⎣⎡​38−6​−1−32​−1−11​⎦⎤​

Question Text	Find the adjoint of matrix $A = ⎣ ⎡ 122130251 ⎦ ⎤$
Answer Type	Text solution:1
Upvotes	150

Find the adjoint of matrix $A = ⎣ ⎡ 122130251 ⎦ ⎤$

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Find the adjoint of matrix A=⎣⎡​122​130​251​⎦⎤​

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Find the adjoint of matrix $A = ⎣ ⎡ 122130251 ⎦ ⎤$