`|[x,y],[alpha,beta]|=0rArr`

If |[x,y],[alpha,beta]|=0 , then, find the relation between x and y.

If alpha,beta are the roots of x^(2)+x+1=0 then det[[beta,y+alpha,1alpha,1,y+beta]]

sin alpha + sin beta = a, cos alpha + cos beta = b rArr sin (alpha + beta)

Let alpha and beta be the roots of the equation x^(2)+x+1=0. Then for y ne 0 in R, |(y+1,alpha,beta),(alpha,y+beta,1),(beta,1,y+alpha)| is equal to :

Let alpha and beta be the roots of the equation x^(2) + x + 1 = 0 . Then, for y ne 0 in R. |{:(y+1, alpha,beta), (alpha, y+beta, 1),(beta, 1, y+alpha):}| is

If alpha,beta,gamma are cube roots of of p<0 then for any real x,y,z;(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

[[(| x + y |) / (| x | + | y |), alpha_ (1), beta_ (1) alpha_ (2), (| y + z |) / (| y | + | z | ), beta_ (2)], (alpha_ (3) | x + z |) / (| x | + | z |), beta_ (3))]]

If alpha and beta are the roots of the equation 1+ x+ x^2 =0, then the matrix product is equal to [[1,beta],[alpha,alpha]].[[alpha,beta],[1,beta]]

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.