The value of determinant `|b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a b-c^2b c-a^2a c-b^2|` is a. always positive b. always negative c. always zero`` d. cannot say anything

The value of the determinant ,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]| is

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Find the factor of determinant |(a, b+c, a^2), (b, c+a, b^2), (c, a+b, c^2)|.

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a b| is divisible by- a. a+b+c b. (a+b)(b+c)(c+a) c. a^2+b^2+c^2 d. (a-b)(b-c)(c-a)

Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^c+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^2+c^2| is always non-negative. When is the determinant zero?