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CBSE Class 12 · 2012 · DeterminantsLong Answer

Using properties of determinants, prove that

1 + a 11 1 1 + b 1 11 1 + c = ab + b c + c a + ab c .

Answer: Proved

Solution

Take

ab c

common after writing each row scaled by

\frac{1}{a}, \frac{1}{b}, \frac{1}{c}

; more directly, apply

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

and

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

:

a 01 0 b 1 - c - c 1 + c .

Expanding along

C_{1}

:

= a (b (1 + c) + c) + 1 (0 \cdot (- c) - b (- c)) = a (b + b c + c) + b c = ab + b c + c a + ab c .

Proved.

CBSE Class 12 Board · 2012 · Subjective

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