Using elementary transformation, the inverse of the matrix [1 2 3 2 5 7 -2 -4 -5] is

Question

Using elementary transformation, the inverse of the matrix [1 2 3 2 5 7 -2 -4 -5] is (A) [3 -3 3 -4 1 -1 2 0 1] (B) [3 -3 3 -4 2 -1 2 0 1] (C) [3 -2 -1 -4 1 -1 2 0 1] (D) [3 -2 1 -4 2 -1 2 0 1]

Tardigrade Admin · Accepted Answer

Let A=[1 2 3 2 5 7 -2 -4 -5] Consider A = IA ∴ [1 2 3 2 5 7 -2 -4 -5]= [1 0 0 0 1 0 0 0 1]A Applying R 2 arrow R 2-2 R 1, R 3 arrow R 3+2 R 1, we get [1 2 3 0 1 1 0 0 1]= [1 0 0 -2 1 0 2 0 1]A Applying R 1 arrow R 1-3 R 3, R 2 arrow R 2- R 3, we get [1 2 0 0 1 0 0 0 1]= [3 -2 -1 -4 1 -1 2 0 1]A Applying R 1 arrow R 1-2 R 2, we get [1 0 0 0 1 0 0 0 1]= [3 -2 -1 -4 1 -1 2 0 1] A ∴ A-1= [3 -2 -1 -4 1 -1 2 0 1]

Q. Using elementary transformation, the inverse of the matrix $⎣ ⎡ 12 - 2 25 - 4 37 - 5 ⎦ ⎤$ is

$⎣ ⎡ 3 - 4 2 - 3 10 3 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 3 20 3 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 2 10 - 1 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 2 20 1 - 1 1 ⎦ ⎤$

Q. Using elementary transformation, the inverse of the matrix ⎣⎡​12−2​25−4​37−5​⎦⎤​ is

⎣⎡​3−42​−310​3−11​⎦⎤​

⎣⎡​3−42​−320​3−11​⎦⎤​

⎣⎡​3−42​−210​−1−11​⎦⎤​

⎣⎡​3−42​−220​1−11​⎦⎤​

Q. Using elementary transformation, the inverse of the matrix $⎣ ⎡ 12 - 2 25 - 4 37 - 5 ⎦ ⎤$ is

$⎣ ⎡ 3 - 4 2 - 3 10 3 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 3 20 3 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 2 10 - 1 - 1 1 ⎦ ⎤$

$⎣ ⎡ 3 - 4 2 - 2 20 1 - 1 1 ⎦ ⎤$