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CBSE Class 12 · 2019 · MatricesLong Answer

Find the inverse of the following matrix using elementary transformations:

A = 250011 - 1 03 .

Answer: $A^{- 1} = 3 - 15 5 - 1 6 - 2 1 - 5 2$

Solution

Write

A = I A

and reduce

A

to

I

with row operations:

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

style pivots, clearing each column while mirroring on the right. The right side becomes

A^{- 1} = 3 - 15 5 - 1 6 - 2 1 - 5 2 .

(One may check

A A^{- 1} = I

.)

CBSE Class 12 Board · 2019 · Subjective

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