If `|b+cc+a a+b a+bb+cc+a c+a a+bb+c|=k|a b cc a bb c a|` , then value of `k` is `1` b. `2` c. `3` d. `4`

Prove: |b+c a a b c+a b cc a+b|=4a b c

Prove that |b+c a a b c+a b cc a+b|=4a b c

- aa bc a - b - c - - bb - c - c

If the determinant |b-cc-a a-bb^(prime)-c ' c^(prime)-a ' a^(prime)-b ' b^-c ' ' c^-a ' ' a^-b ' '|=m|a b c a ' b ' c ' a ' ' b ' ' c ' '| , then the value of m s 0 b. 2 c. 1 d. -1

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

If a ,b , c are nonzero real numbers such that |b cc a a b c a a bb c a bb cc a|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega^)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

If ab:b+c:c+a=6:7:8backslash and backslash a+b+c=14 then the value of c is 6b.7c.8d.14

If a+b:b+c:c+a = 6:7:8 anda + b+ c =14, then find c.

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?