Let alpha be a root of the equation x ^(2) - x+1=0, and the matrix A=[{:(1,1,1),(1, alpha , alpha ^(2)), (1, alpha ^(2), alpha ^(4)):}] and matrix B= [{:(1,-1, -1),(1, alpha, - alpha ^(2)),(-1, -alpha ^(2), - alpha ^(4)):}] then the vlaue of |AB| is:
Let alpha be a root of the equation x ^(2) + x + 1 = 0 and the matrix A = ( 1 ) /(sqrt3) [{:( 1,,1,,1),( 1,, alpha ,, alpha ^(2)), ( 1 ,, alpha ^(2),, alpha ^(4)):}] then the matrix A ^( 31 ) is equal to :
Let alpha, beta be the roots of equation x ^ 2 - x + 1 = 0 and the matrix A = (1 ) /(sqrt3 ) |{:(1,,1,,1),(1,,alpha,,alpha ^2),(1,,beta,,-beta^ 2):}| , the value of det (A. A^T) is
If alpha,beta are two roots of equation 5x^(2)-7x+1=0, then (1)/(alpha)+(1)/(beta) is
If alpha is a root of the equation 4x^(2)+2x-1=0 and f(x)=4x^(2)-3x+1 , then 2(f(alpha)+(alpha)) is equal to
If alpha and beta are the roots of the equation 4x^(2)+3x+7=0, then (1)/(alpha)+(1)/(beta)=
If alpha and beta are the roots of the equation 3x^(2)+8x+2=0 then ((1)/(alpha)+(1)/(beta))=?
If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=
If alpha and beta are the roots of the equation 1+x+x^(2)=0 , then the matrix product [{:(1, beta),(alpha,alpha):}][{:(alpha, beta),(1,beta):}] is equal to :
