9. Linear Transformations

Testing Linearity — Quiz

Test your understanding of testing linearity with 5 practice questions.

Practice Questions

Question 1

If $T:\mathbb{R}^2\to\mathbb{R}^2$ is linear, what must $T(\mathbf{0})$ equal?

Question 2

Why is $T(x)=x+1$ not linear as a map from $\mathbb{R}$ to $\mathbb{R}$?

Question 3

If $T$ is linear and $T(\mathbf{u})=\mathbf{a}$ and $T(\mathbf{v})=\mathbf{b}$, what is $T(\mathbf{u}+\mathbf{v})$?

Question 4

If $T$ is linear and $T(\mathbf{v})=\mathbf{w}$, what is $T(3\mathbf{v})$?

Question 5

Which map is linear?