Q19 of 45 Page 1

Using properties of determinants, prove the following:

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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