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CBSE Class 12 · 2013 · MatricesLong Answer

Using elementary operations, find the inverse of the following matrix:

- 1 13 121231

Answer: $A^{- 1} = 1 - 8 5 - 1 7 - 4 1 - 5 3$

Solution

Write

A = I A

and reduce

A

to

I

by row operations. Using

R_{1} \leftrightarrow R_{2}

, then

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

,

R_{3} \to R_{3} - 3 R_{1}

, and a sequence of pivots to clear each column, the right side becomes

A^{- 1} = 1 - 8 5 - 1 7 - 4 1 - 5 3 .

CBSE Class 12 Board · 2013 · Subjective

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