Prove that `|(2,alpha+beta+gamma+delta,alphabeta+gammadelta),(alpha+beta+gamma+delta,2(alpha+beta)(gamma+delta),alpha beta(gamma+delta)+gamma delta(gamma+beta)),(alpha beta+gamma delta,alpha beta(gamma+delta)+gammadelta(alpha+beta),2alphabeta gamma delta)|` = 0

Consider Delta=|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)| Show that Delta=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma) .

Using properties of determinants, prove that |[alpha, alpha^2, beta+gamma],[beta,beta^2,gamma+alpha],[gamma,gamma^2,alpha+beta]|=(beta-gamma)(gamma-alpha)(alpha-beta)(alpha+beta+gamma)

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix Find A^T

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix If A^T.A=6I, then alpha,beta and gamma is -

Consider Delta=|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)| Apply R_3rarrR_1+R_3

If x= (beta -gamma )(alpha -delta ), y= (gamma - alpha)(beta -delta ), z=(alpha -beta) (gamma - delta ) then the value of x^(3) +y^(3) +z^(3) -3xyz is : a)0 b) alpha ^(6) +beta ^(6) +gamma ^(6) delta ^(6) c) alpha ^(6) beta^(6) gamma ^(6)delta^(6) d)1

If a, b and c are in geometric progression and the roots of the equations ax^(2)+2bx+c=0 are alpha and beta and those cx^(2)+2bx+a=0 are gamma and delta , then : a) alpha ne beta ne gamma ne delta b) alpha ne beta and gamma ne delta c) alpha=abeta=cgamma=cdelta d) alpha=beta and gamma ne delta

If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I , then A) 1+alpha^2+beta gamma=0 B) 1-alpha^2+beta gamma=0 C) 1-alpha^2-beta gamma=0^ D) 1+alpha^2-beta gamma=0

|(alpha,-beta,0),(0,alpha,beta),(beta,0,alpha)|=0 , then

If alpha, beta, gamma are the roots of ax^(3) + bx^(2) + cx + d = 0 and |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| = 0, alpha != beta != gamma , then find the equation whose roots are alpha + beta - gamma, beta + gamma - alpha and gamma + alpha - beta