Q. 133.8( 19 Votes )

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Answer :

Consider Using the property that if the equalities of corresponding elements of other rows (or columns) are added to every element of any row (or column) of a determinant, then the value of determinant remains the same

Using column transformation, C1C1+C2+C3

we get, Using the property that if each element of a row (or a column) of a determinant is multiplied by a constant k, then its value gets multiplied by k.

Taking out factor (a + b + c) from C1,

we get, Using row transformation, R3R3-2R1

we get, Expanding along C1, we get

∆= (a + b + c)[(b-c)(a+b-2c)-(c-a)(c+a-2b)]

= (a + b + c)[ab+b2-2bc-ac-bc+2c2-c2-ac+2bc+ac+a2-2ab]

= (a + b + c)[a2+b2+c2-ab-bc-ac]

= a3+b3+c3-3abc

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