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Find the inverse of the matrices , if it exists. {bmatrix} 2

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Find the inverse of the matrices , if it exists.
$[2537]$

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Find the inverse of the matrices , if it exists.

[2537]

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Text solutionVerified

Let

A = [2537]

We know that

A = I A

∴ A = [2537] = [1001] A

\Rightarrow [15 \frac{3}{2} 7] = [\frac{1}{2} 0 01] A (R_{1} \to \frac{1}{2} R_{1})

\Rightarrow [10 \frac{3}{2} - \frac{1}{2}] = [\frac{1}{2} - \frac{5}{2} 01] A (R_{2} \to R_{2} - 5 R_{1})

\Rightarrow [10 0 - \frac{1}{2}] = [- 7 - \frac{5}{2} 31] A (R_{1} \to R_{1} - 3 R_{2})

\Rightarrow [10 0 \frac{1}{2}] = [- 7 \frac{5}{2} 3 - 1] A (R_{2} \to - R_{2})

\Rightarrow [1001] = [- 7 5 3 - 2] A (R_{2} \to 2 R_{2})

∴ A^{- 1} = [- 7 5 3 - 2]

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Question Text	Find the inverse of the matrices , if it exists. $[2537]$
Answer Type	Text solution:1
Upvotes	150