Using properties of determinants, prove the following : \left|\begin{array}{c}{\a\end{array}+ {\b}+ {\c} , - {\c} , - {\b} ; - {\c} , {\a}+ {\b}+ {\c} , - {\a} ; - {\b} , - {\a} , {\a}+ {\b}+ {\c} |}=2( {\a}+ {\b})( {\b}+ {\c})( {\c}+ {\a}) \text{. }

CBSE Class 12 Math 2019 Delhi Set 2 Solved Paper - Question 6

Question : 6 of 9

Marks: +1, -0

Using properties of determinants, prove the following :

{|\table {\a}+ {\b}+ {\c} , - {\c} , - {\b} ; - {\c} , {\a}+ {\b}+ {\c} , - {\a} ; - {\b} , - {\a} , {\a}+ {\b}+ {\c} |}=2( {\a}+ {\b})( {\b}+ {\c})( {\c}+ {\a}) \;\text ". "\;

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