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CBSE Class 12 · 2011 · DeterminantsLong Answer

Using the properties of determinants, prove that

x + 4 2 x 2 x 2 x x + 4 2 x 2 x 2 x x + 4 = (5 x + 4) (4 - x)^{2} .

Answer: Proved

Solution

Apply

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

so that column

1

is entirely

5 x + 4

; take it common.

= (5 x + 4) 111 2 x x + 4 2 x 2 x 2 x x + 4 .

Then

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

,

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

gives an upper-triangular block:

= (5 x + 4) 100 2 x 4 - x 0 2 x 0 4 - x = (5 x + 4) (4 - x)^{2} .

Proved.

CBSE Class 12 Board · 2011 · Subjective

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