9. Linear Transformations

Rank And Nullity — Quiz

Test your understanding of rank and nullity with 5 practice questions.

Practice Questions

Question 1

For a linear transformation $T:V\to W$, what does the rank of $T$ measure?

Question 2

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

Question 3

If $T:\mathbb{R}^3\to\mathbb{R}^5$ has rank $2$, what is its nullity?

Question 4

If a matrix $A$ has $3$ columns and rank $2$, how many free variables are in the system $Ax=0$?

Question 5

If $T:\mathbb{R}^4\to\mathbb{R}^4$ has nullity $1$, what is its rank?