Show that if `lambda_1, lambda_2, ..., lambda_n` are`n` eigen values of a square matrix `A` of order `n` then the eigen values of the matrix `A^2` are `lambda_1^2, lambda_2^2, .... , lambda_n^2`

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) .

If A is a square matrix of order nxxn such that |A|=lambda , then write the value of |-A| .

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

If lambda_1 and lambda_2 , are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of lambda_1:lambda_2 is:

if ._(1)mu_2 is 1.5, then find the value of lambda_1/lambda_2.

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

For a non zero " lambda" ,the value of matrix "[[lambda,1,0],[0,lambda,1],[0,0,lambda]]^(n) " is equal to

The point (lambda+1,1),(2 lambda+1,3) and (2 lambda+2,2 lambda) are collinear,then the value of lambda can be

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