The value of determinant vmatrixa-b&b+c&a\ -a&c+a&b\ -a&a+b&c vmatrix is

Question

Accepted Answer

Correct answer: C. (c): Let =(a-bb+cab-ac+abc-aa+bc) Applying C_1 C_1-C_3 and C_2 C_2+C_3, we get =(-ba+b+ca-aa+b+cb-aa+b+cc) Taking common (a+b+c ) from C_2 we get, = (a+b+c )(-b1a-a1b-a1c) Applying R_2 R_2-R_1 and R_3 R_3-R_1 = (a+b+c )(-b1ab-a0b-ab-a0c-a) Expanding along C_2, we get =- (a+b+c )( (b-a ) (c-a )- (b-a )^2) =- (a+b+c ) (b-a ) [c-a-b+a ] =- (a+b+c ) (b-a ) (c-b ) = (a+b+c ) (a-b ) (c-b )

$The value of determinant a - b b - a c - a b + c c + a a + b a b c is$

Solution

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