Q. 195.0( 1 Vote )

# Using properties of determinants, prove the following:

Answer :

Let Δ =

Multiply and divide by xyz such that R_{1}→ xR_{1,} R_{2}→ yR_{2}, R_{3}→ zR_{3}

Now,

Δ =

Taking out x,yand z common from C_{1}, C_{2} and C_{3}respectively,we get

Δ =

Applying R_{1}→ R_{1+}R_{2} + R_{3}, we get

Δ =

Applying C_{2}→ C_{2} – C_{1} and C_{3}→ C_{3} – C_{1}, we get

Δ =

Expanding along R_{1}, we get

Δ = 1+x^{2}+y^{2}+z^{2} (1-0)

= 1+x^{2}+y^{2}+z^{2}

= RHS

Hence proved.

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