Question

H, could anyone help me look at the following question? part (iv) and (v)
attached question

Answer 1

I got the smallest possible answer of k is 3. not sure whether it is correct or not

Answer 2

part (ii) the smallest possible answer.

Answer 3

3 is correct

Answer 4

For iii) I got
\[
B^{-1} = \frac 1 {\lambda^3}B^2 - \frac 3{\lambda^2}B + \frac 3\lambda I

\]

Answer 5

For iv)
\[
V_n

\]
is the null space of the matrix \[
(B- \lambda I)^n
\]

Answer 6

So it is a subspace

Answer 7

For v)
n=3

Answer 8

If you need more details, let me know

Answer 9

thank you so much, prof! I'll take a look first.

Answer 10

yw