Question

If the eigen values of a matrix A are 1, 3, 4 then find the eigen values of A –1 and A 3 .

Answer 1

Step-by-step explanation:

Let v1,v2,v3 be the eigenvectors of A with the corresponding eigenvalues λi=1,2,3 . Note that A⊤ has the same eigenvalues as A .

Then, Bvi=(A2+A⊤)vi =A2vi+A⊤vi=(λ2i+λi)vi . Hence, the eigenvalues of B are νi=λ2i+λi . Hence |B|=ν1ν2ν3=144 .