Q13 of 45 Page 1

Using properties of determinants, prove that

Let


Interchanging R2 and R3 then R1 and R2, we get



Applying R1 → R1 + R2 + R3, we get



Taking out (x+y+z) common from R1, we get



Applying C1→ C1 - C2 and C2→ C2- C3, we get



Expanding along R1, we get


Δ =


Δ = (x+y+z) (y+z+x)2


Δ = (x+y+z)3


= RHS


Hence proved.


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