Let a, b, and c be three real numbers satifying `[(a, b, c)]`
`[(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
Let `omega` be a solution of `x^(3)-1=0` with `Im (omega) gt 0`. If `a=2` with b and c satisfying (E), then the value of `3/omega^(a)+1/omega^(b)+3/omega^(c)` is equal to

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let omega be a solution of x^3-1=0 with Im(omega)gt0. I fa=2 with b nd c satisfying (E) then the vlaue of 3/omega^a+1/omega^b+3/omega^c is equa to (A) -2 (B) 2 (C) 3 (D) -3

Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0 . If a=2 with b and c satisfying [abc][{:(1,9,7),(2,8,7),(7,3,7):}]=[0,0,0] , then the value of 3/omega^(a) + 1/omega^(b) + 1/omega^( c) is equal to

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] If the point P(a,b,c) with reference to (E), lies on the plane 2x+y+z=1 , the the value of 7a+b+c is (A) 0 (B) 12 (C) 7 (D) 6

Let a, b and c be three real numbers satisfying [a" "b" "c"][{:(1,9,7),(8,2,7),(7,9,7):}]=[0"" "0""" "0] and alpha and beta be the roots of the equation ax^(2) + bx + c = 0 , then sum_(n=0)^(oo) ((1)/(alpha)+(1)/(beta))^(n) , is

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let b=6, with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n is (A) 6 (B) 7 (C) 6/7 (D) oo

Let p,q,r in R satisfies [p q r][(1,8,7),(9,2,3),(7,7,7)] = [0 0 0] .....(i) {:(,"List-I",,"List-I"),((P),"If the point M(p.q.r) with reference to (i) lies on the curve" 2x+y+z=1 then (7p+q+r) "is equal to",(1),-2),((Q),"Let" omega(ne1) "cube root of unity with" lm(omega) gt0.If p=2 "with q and r satisfying" (i) then (3/(omega^(p))+1/(omega^(q))+3/(omega^(r))) "is equal to ",(2),7),((R),"Let q=6 with p and r satisfying"(i). if alpha and beta "are roots of quadratic equation " px^(2)+qx+r=0 " then" Sigma_(n=0)^(oo) (1/(alpha)+1/(beta))^(n) " is equal to ",(3),6):}

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

Find the complex number satisfying the system of equations z^3+ omega^7=0a n dz^5omega^(11)=1.

Prove the following (a + b omega + c omega^(2))/(b + c omega + a omega^(2))= omega

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)