The value of the determinant `|(1+a, 1, 1),(1, 1+a, 1),(1, 1, 1+a)|` is zero if (A) `a=-3` (B) `a=0` (C) `a=2` (D) `a=1`

The value of the determinant |{:(1,0,-1),(a,1,1-a),(b,a,1+a-b):}| depends on :

if the value of the determinant |{:(a,,1,,1),(1,,b,,1),(1,,1,,c):}| is positivie then (a,b,c lt 0)

Let omega=-1/2+i(sqrt(3))/2 . Then the value of the determinant |(1,1,1),(1,-1-omega^2,omega^2),(1,omega^2,omega^4)| is (A) 3omega (B) 3omega(omega-1) (C) 3omega^2 (D) 3omega(1-omega)

If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive then a. a b c >1 b. a b c> -8 c. a b c -2

If C = 2 cos theta , then the value of the determinant Delta = |(C,1,0),(1,C,1),(6,1,c)| , is

Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1],[ 1,-1-omega^2,-omega^2],[1, omega^2,omega^4]] is (a) 3omega (b) 3omega(omega-1) (c) 3omega^2 (d) 3omega(1-omega)

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1,1 +b,1),(1,1,1 +c)| = 0 , then the value of (1)/(a) + (1)/(b) + (1)/(c) is

The value of the determinant |(1,1,1),(.^(m)C_(1),.^(m +1)C_(1),.^(m+2)C_(1)),(.^(m)C_(2),.^(m +1)C_(2),.^(m+2)C_(2))| is equal to

Given a skew symmetric matrix A = [ (0, a , 1),(-1, b, 1),(-1, c, 0)] , the value of (a + b + c)^2 is