Exercise 5.2.11

Answers

1.

Since eigenvalues are the zeroes of the characteristic polynomial, we may write the characteristic polynomial

f (t)

{(λ_{1} - t)}^{m_{1}} {(λ_{2} - t)}^{m_{2}} \dots {(λ_{k} - t)}^{m_{k}} .

Calculate the coefficient of $t^{n - 1}$ and use the fact in Exercise 5.1.21(b). Thus we could get the desired conclusion.

2.

Use the equality in the previous exercise and calculate the coefficient of the constant term. Compare it to the Exercise 5.1.20.

jephianlin

2011-06-27 00:00