Q. 195.0( 1 Vote )

Using properties of determinants, prove the following:

Answer :

Let Δ =

Multiply and divide by xyz such that R1 xR1, R2 yR2, R3 zR3


Δ =

Taking out x,yand z common from C1, C2 and C3respectively,we get

Δ =

Applying R1 R1+R2 + R3, we get

Δ =

Applying C2 C2 – C1 and C3 C3 – C1, we get

Δ =

Expanding along R1, we get

Δ = 1+x2+y2+z2 (1-0)

= 1+x2+y2+z2


Hence proved.

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