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


Now,


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


= RHS


Hence proved.


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