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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.
$[2153]$

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Find the inverse of the matrices, if it exists.

[2153]

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Text solutionVerified

Let

A = [2153]

We know that

A = I A

∴ A = [2153] = [1001] A

\Rightarrow [11 \frac{5}{2} 3] = [\frac{1}{2} 0 01] A (R_{1} \to \frac{1}{2} R_{1})

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

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

\Rightarrow [1001] = [3 - 1 - 5 2] A (R_{2} \to 2 R_{2})

∴ A^{- 1} = [3 - 1 - 5 2]

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Question Text	Find the inverse of the matrices, if it exists. $[2153]$
Answer Type	Text solution:1
Upvotes	150