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CBSE Class 12 · 2011 · DeterminantsLong Answer

Using the properties of determinants, solve the following for

x

:

x - 2 x - 4 x - 8 2 x - 3 2 x - 9 2 x - 27 3 x - 4 3 x - 16 3 x - 64 = 0.

Answer: $x = 4$

Solution

Apply

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

and

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

to simplify.

x - 2 - 2 - 6 2 x - 3 - 6 - 24 3 x - 4 - 12 - 60 = 0.

Take

- 2

from

R_{2}

and

- 6

from

R_{3}

, then

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

:

12 x - 2 10 2 x - 3 31 3 x - 4 64 = 0.

Expanding gives a linear equation whose root is

x = 4

.

x = 4

CBSE Class 12 Board · 2011 · Subjective

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