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CBSE Class 12 · 2018 · MatricesLong Answer

Using elementary row transformations, find the inverse of the matrix

A = 12 - 2 25 - 4 37 - 5

.

Answer: $A^{- 1} = 3 - 4 2 - 2 10 - 1 - 1 1$ \,

Solution

Write

A = I A

. Apply

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

,

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

to get a unit pivot column, then

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

, and finally

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

,

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

. The right-hand matrix becomes

A^{- 1} = 3 - 4 2 - 2 10 - 1 - 1 1 .

CBSE Class 12 Board · 2018 · Subjective

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