Exercises: Work with 2x2 Matrices as Transformations

Work through each section in order. Show your work where indicated.

Grade 9·20 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-12

Work through problems with immediate feedback

Recall / Warm-Up

To understand what a $2 \times 2$ matrix $A$ does to the entire plane, you need to track only two special vectors. Which two?

The first and last rows of $A$

The standard basis vectors $\mathbf{e}_1 = \begin{bmatrix}1\\0\end{bmatrix}$ and $\mathbf{e}_2 = \begin{bmatrix}0\\1\end{bmatrix}$

Any two perpendicular vectors

The zero vector and the vector of all ones