The inverse of the matrix [2&5&0 0&1&1 -1&0&3] is

Question

The inverse of the matrix [2&5&0 0&1&1 -1&0&3] is (A) [3&-15&5 -1&6&-2 1&-5&2] (B) [3&-1&1 -15&6&-5 5&-2&2] (C) [3&-15&5 -1&6&-2 1&-5&-2] (D) [3&-5&5 -1&-6&-2 1&-5&2]

Tardigrade Admin · Accepted Answer

Let A=[ beginmatrix2&5&0 0&1&1 -1&0&3 endmatrix] |A|=2(3-0)-5(0+1) = 6 - 5 = 1 ∴ |A|=1 adj A=[ beginmatrix3&-1&1 -15&6&-5 5&-2&2 endmatrix]T=[ beginmatrix3&-15&5 -1&6&-2 1&-5&2 endmatrix] A-1=(adj A/|A|)=[ beginmatrix3&-15&5 -1&6&-2 1&-5&2 endmatrix]

Q. The inverse of the matrix $⎣ ⎡ 20 - 1 510013 ⎦ ⎤$ is

$⎣ ⎡ 3 - 1 1 - 15 6 - 5 5 - 2 2 ⎦ ⎤$

$⎣ ⎡ 3 - 15 5 - 1 6 - 2 1 - 5 2 ⎦ ⎤$

$⎣ ⎡ 3 - 1 1 - 15 6 - 5 5 - 2 - 2 ⎦ ⎤$

$⎣ ⎡ 3 - 1 1 - 5 - 6 - 5 5 - 2 2 ⎦ ⎤$

$L e t A = ⎣ ⎡ 20 - 1 510013 ⎦ ⎤$
$∣ A ∣ = 2 (3 - 0) - 5 (0 + 1)$
$= 6 - 5 = 1$
$∴ ∣ A ∣ = 1$
$a d j A = ⎣ ⎡ 3 - 15 5 - 1 6 - 2 1 - 5 2 ⎦ ⎤^{T} = ⎣ ⎡ 3 - 1 1 - 15 6 - 5 5 - 2 2 ⎦ ⎤$
$A^{- 1} = \frac{a d j A}{∣ A ∣} = ⎣ ⎡ 3 - 1 1 - 15 6 - 5 5 - 2 2 ⎦ ⎤$

Q. The inverse of the matrix ⎣⎡​20−1​510​013​⎦⎤​ is

⎣⎡​3−11​−156−5​5−22​⎦⎤​

⎣⎡​3−155​−16−2​1−52​⎦⎤​

⎣⎡​3−11​−156−5​5−2−2​⎦⎤​

⎣⎡​3−11​−5−6−5​5−22​⎦⎤​