EXAMPLE 29 Prove that 62 ca = 0.
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EXAMPLE 29 Prove that 62 ca = 0.

11th - 12th Class
Maths
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104
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solution Let the given determinant be ( Delta ). Then, [ begin{aligned} Delta &=left|begin{array}{lll} frac{1}{a} & a^{2} & b c frac{1}{b} & b^{2} & c a frac{1}{c} & c^{2} & a b end{array}right| =frac{1}{a b c} & begin{array}{lll} 1 & a^{3} & a b c 1 & b^{3} & text { cba } 1 & c^{3} & a b c end{array} mid & text { [multiplying } R_{1}, R_{2}, R_{3} text { by } a, b & text { respectively and dividing } Delta text { by } end{aligned} ] [ =frac{1}{a b c} cdot a b c cdotleft|begin{array}{ccc} 1 & a^{3} & 1 1 & b^{3} & 1 1 & c^{3} & 1 end{array}right| ] ( =(1 times 0)=0 quadleft[because C_{1} text { and } C_{3} ) are identical] right. Hence, ( Delta=0 )
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