## anonymous one year ago For fun

1. anonymous

Which of the following are eigenpairs (λ,x) of the 2×2 zero matrix: $\left[\begin{matrix}0 & 0 \\ 0 & 0\end{matrix}\right]=$where $\chi \neq0$

2. anonymous

$\left[\begin{matrix}0 & 0 \\ 0 & 0\end{matrix}\right]\chi= \lambda \chi$where $\chi \neq0$

3. anonymous

A. $(1,\left(\begin{matrix}0 \\ 0\end{matrix}\right))$B.$(0,\left(\begin{matrix}1 \\ 0\end{matrix}\right))$C$(0,\left(\begin{matrix}0 \\ 1\end{matrix}\right))$D$(0,\left(\begin{matrix}-1 \\ 1\end{matrix}\right))$E$(0,\left(\begin{matrix}1 \\ 1\end{matrix}\right))$F$(0,\left(\begin{matrix}0 \\ 0\end{matrix}\right)$

4. ganeshie8

$\left[\begin{matrix}0 & 0 \\ 0 & 0\end{matrix}\right]\chi= \lambda \chi$where $\chi \neq0$ Notice that the left hand side evaluates to zero vector no matter what the vector $$\chi$$ is, so it follows that $$\lambda = 0$$

5. anonymous

yea

6. anonymous

i know the answers actually so just for fun :)

7. anonymous

pick the options which are eigenpairs

8. ganeshie8

By definition, eigenvector cannot be zero, so the last option can be eliminated

9. anonymous

you mean first and last, both are 0

10. ganeshie8

Ahh right, first and last options are eliminated

11. ganeshie8

remaining all options look good to me!

12. anonymous

That's correct!

13. ganeshie8

yaay!