11. Eigenvalues and Eigenvectors

Eigenspaces — Quiz

Test your understanding of eigenspaces with 5 practice questions.

Practice Questions

Question 1

What is the eigenspace of a matrix $A$ for an eigenvalue $\lambda$?

Question 2

Which vector must always belong to every eigenspace of $A$?

Question 3

Let $A=\begin{pmatrix}2&0\\0&3\end{pmatrix}$. Which set is the eigenspace for $\lambda=2$?

Question 4

If $v$ is in the eigenspace for $\lambda$ and $c\neq 0$, where does $cv$ belong?

Question 5

For the $2\times 2$ identity matrix $I$, what is the eigenspace for $\lambda=1$?