9. Linear Transformations

Interpreting Rank-nullity Conceptually — Quiz

Test your understanding of interpreting rank-nullity conceptually with 5 practice questions.

Practice Questions

Question 1

Which statement is the rank-nullity theorem for a linear transformation $T:V\to W$ when $V$ is finite-dimensional?

Question 2

A linear transformation $T:\mathbb{R}^5\to\mathbb{R}^3$ has rank $3$. What is its nullity?

Question 3

If a linear transformation $T$ has nullity $0$, what is true about $T$?

Question 4

A linear transformation $T:\mathbb{R}^7\to W$ has rank $2$. What is its nullity?

Question 5

For a linear transformation, what does the nullity measure?