Question

For fun

Answer 1

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 \[\chi \neq0\]

Answer 2

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

Answer 3

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\[(0,\left(\begin{matrix}0 \\ 0\end{matrix}\right)\]

Answer 4

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

Notice that the left hand side evaluates to zero vector no matter what the vector \(\chi \) is, so it follows that \(\lambda = 0\)

Answer 5

yea

Answer 6

i know the answers actually so just for fun :)

Answer 7

pick the options which are eigenpairs

Answer 8

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

Answer 9

you mean first and last, both are 0

Answer 10

Ahh right, first and last options are eliminated

Answer 11

remaining all options look good to me!

Answer 12

That's correct!

Answer 13

yaay!