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

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) .

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

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

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

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 If A^T.A=6I, then alpha,beta and gamma is -

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

If alpha+beta =pi//2andbeta+gamma=alpha , then tanalpha equals

If alpha , beta , lambda are three real numbers and A=[(1,cos(alpha-beta),cos(alpha-gamma)),(cos(beta-alpha),1,cos(beta-gamma)),(cos(gamma-alpha),cos(gamma-beta),1)] , then which of following is not true A)A is singular B)A is symmetric C)A is orthogonal D)A is not invertible