Show that if `lambda_(1), lambda_(2), ...., lamnda_(n)` are `n` eigenvalues of a square matrix a of order n, then the eigenvalues of the matric `A^(2)` are `lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2)`.

Show that if lambda_(1), lambda_(2), ...., lambda_(n) are n eigenvalues of a square matrix a of order n, then the eigenvalues of the matric A^(2) are lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2) .

" If "A" is a square matrix of order "n" ,then "|adj[lambda A)|" is equal to "

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

Two particle are moving perpendicular to each with de-Broglie wave length lambda_(1) and lambda_(2) . If they collide and stick then the de-Broglie wave length of system after collision is : (A) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (B) lambda = (lambda_(1))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (C) lambda = (sqrt(lambda_(1)^(2) + lambda_(2)^(2)))/(lambda_(2)) (D) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1) + lambda_(2)))

Two particle are moving perpendicular to each with de-Broglie wave length lambda_(1) and lambda_(2) . If they collide and stick then the de-Broglie wave length of system after collision is : (A) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (B) lambda = (lambda_(1))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (C) lambda = (sqrt(lambda_(1)^(2) + lambda_(2)^(2)))/(lambda_(2)) (D) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1) + lambda_(2)))

If alpha, beta are the roots of the equation lambda(x^(2)-x)+x+5=0 and if lambda_(1) and lambda_(2) are two values of lambda obtained from (alpha)/(beta)+(beta)/(alpha)=(4)/(5) , then (lambda_(1))/(lambda_(2)^(2))+(lambda_(2))/(lambda_(1)^(2)) equals

If lambda_(1) and lambda_(2) be two values of lambda for which the expression x^(2)+(2-lambda) x+lambda-(3)/(4) becomes a perfect square, then calculate the value of (lambda_(1)^(2)+lambda_(2)^(2)) .

If lambda_(1) and lambda_(2) are the wavelengths of the first members of the Lyman and Paschen series respectively, then lambda_(1) : lambda_(2) is