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CBSE Class 12 · 2011 · MatricesLong Answer

Using elementary transformations, find the inverse of the matrix

1 - 3 2 301 - 2 - 1 0

.

Answer: $A^{- 1} = 1 - 2 - 3 - 2 45 - 3 79$

Solution

Write

A = I A

and reduce

A

to

I

by row operations, mirroring them on the right.
Apply

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

,

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

; then

R_{1} \to R_{1} - \frac{1}{3} R_{2}

,

R_{2} \to \frac{1}{9} R_{2}

; then

R_{3} \to R_{3} + 5 R_{2}

; then

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

,

R_{2} \to R_{2} + 7 R_{3}

,

R_{3} \to 9 R_{3}

. The right side becomes

A^{- 1} = 1 - 2 - 3 - 2 45 - 3 79 .

CBSE Class 12 Board · 2011 · Subjective

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