24. Differentiation and Extension

Extension Opportunities — Quiz

Test your understanding of extension opportunities with 5 practice questions.

Practice Questions

Question 1

What does the nullity of a linear transformation $T:V\to W$ measure?

Question 2

If a linear map $T:\mathbb{R}^3\to\mathbb{R}^2$ has rank $2$, what is its nullity?

Question 3

Suppose $A=[T]_B$ and $P$ is the change-of-basis matrix satisfying $[v]_B=P[v]_C$ for every vector $v$. What is the matrix of $T$ in the basis $C$?

Question 4

What is the characteristic polynomial of the matrix $\begin{pmatrix}0&-1\\1&0\end{pmatrix}$?

Question 5

Which statement describes the structure of a Jordan block for eigenvalue $\lambda$?