If A =[ beginmatrix1&3&5 3&5&1 5&1&3 endmatrix], then adj A is equal to

Question

If A =[ beginmatrix1&3&5 3&5&1 5&1&3 endmatrix], then adj A is equal to (A) [ beginmatrix14&-4&-22 -4&-22&14 -22&14&-4 endmatrix]  (B) [ beginmatrix-14&4&22 4&22&-14 22&-14&4 endmatrix] (C) [ beginmatrix14&4&-22 4&-22&-14 -22&-14&-4 endmatrix]  (D) None of these

Tardigrade Admin · Accepted Answer

We have, A =[ beginmatrix1&3&5 3&5&1 5&1&3 endmatrix] ⇒ adj A =[ beginmatrix14&-4&-22 -4&-22&14 -22&14&-4 endmatrix]

Q. If A = $⎣ ⎡ 135351513 ⎦ ⎤$ , then adj A is equal to

$⎣ ⎡ 14 - 4 - 22 - 4 - 22 14 - 22 14 - 4 ⎦ ⎤$

$⎣ ⎡ - 14 422 422 - 14 22 - 14 4 ⎦ ⎤$

$⎣ ⎡ 144 - 22 4 - 22 - 14 - 22 - 14 - 4 ⎦ ⎤$

None of these

We have, $A = ⎣ ⎡ 135351513 ⎦ ⎤$

$\Rightarrow a d j A = ⎣ ⎡ 14 - 4 - 22 - 4 - 22 14 - 22 14 - 4 ⎦ ⎤$

Q. If A =⎣⎡​135​351​513​⎦⎤​, then adj A is equal to

⎣⎡​14−4−22​−4−2214​−2214−4​⎦⎤​

⎣⎡​−14422​422−14​22−144​⎦⎤​

⎣⎡​144−22​4−22−14​−22−14−4​⎦⎤​