Q31 of 110 Page 260

Using properties of determinants prove that:


Taking a, b, c from C1, C2, C3



Operating R1→R1-R3, R2→R2-R3



Taking (a2+b2+c2) common from R1, R2



Operating R3→R3+R1+R2



Taking (a2+b2+c2) common from C3 �



Expanding with C3


= abc(a2+b2+c2)3×1×(1-0)


= abc (a2+b2+c2)3


Hence proved


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