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CBSE Class 12 · 2010 · MatricesLong Answer

Using elementary row operations, find the inverse of the matrix

A = [2153]

.

Answer: $A^{- 1} = [3 - 1 - 5 2]$ \,

Solution

Write

A = I A

and reduce the left side to

I

by row operations, applying the same operations to the right.

[2153] = [1001] A .

R_{1} \leftrightarrow R_{2}

, then

R_{2} \to R_{2} - 2 R_{1}

, then

R_{1} \to R_{1} + 3 R_{2}

, then

R_{2} \to - R_{2}

gives

[1001] = [3 - 1 - 5 2] A \Rightarrow A^{- 1} = [3 - 1 - 5 2] .

CBSE Class 12 Board · 2010 · Subjective

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