Exercise 5.1.22

Answers

1.

Use the notation

x

and

λ

that in this question. In Exercise 5.1.15(a) we already have

T^{m} (x) = λ^{m} x .

And it’s also easy to see that if $Ax = λ_{1} x$ and $Bx = λ_{2} x$ , we’ll have

(A + B) x = λ_{1} + λ_{2} .

So we get the desired result.

2.

Shit! It’s not funny! Just change

T

into

A

3.

Just calculate that

g (A) = (\begin{matrix} 14 & 10 \\ 15 & 19 \end{matrix})

and

g (A) (\begin{matrix} 2 \\ 3 \end{matrix}) = 29 (\begin{matrix} 2 \\ 3 \end{matrix}) .

Also check that $λ = 4$ and $g (4) = 29$ .

jephianlin

2011-06-27 00:00