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Let A ={bmatrix}1 & -1&1 2& 1 &-3 1 & 1 &1 {bmatrix} and 1

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Let A = $⎣ ⎡ 121 - 1 11 1 - 3 1 ⎦ ⎤$ and 10 B= $⎣ ⎡ 4 - 5 1 20 - 2 2 α 3 ⎦ ⎤$ . If B is the inverse of matrix A, then $α$ is

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Jack Discussed

Let A =

⎣ ⎡ 121 - 1 11 1 - 3 1 ⎦ ⎤

and 10 B=

⎣ ⎡ 4 - 5 1 20 - 2 2 α 3 ⎦ ⎤

. If B is the inverse of matrix A, then

α

6 mins ago

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Text solutionVerified

Given

B = A^{- 1}

\Rightarrow A B = I

\Rightarrow 10 A B = 10 I

\Rightarrow ⎣ ⎡ 121 - 1 11 1 - 3 1 ⎦ ⎤ ⎣ ⎡ 4 - 5 1 20 - 2 2 α 3 ⎦ ⎤ = ⎣ ⎡ 100001000010 ⎦ ⎤

comparing first row third element on both sides gives

2 - α + 3 = 0

∴ α = 5

Hence, option D.

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Question Text	Let A = $⎣ ⎡ 121 - 1 11 1 - 3 1 ⎦ ⎤$ and 10 B= $⎣ ⎡ 4 - 5 1 20 - 2 2 α 3 ⎦ ⎤$ . If B is the inverse of matrix A, then $α$ is
Answer Type	Text solution:1
Upvotes	150