4. Matrix Algebra

Understanding Composition Through Matrices — Quiz

Test your understanding of understanding composition through matrices with 5 practice questions.

Practice Questions

Question 1

If you apply the transformation represented by $A$ first and then the transformation represented by $B$, which matrix represents the composition?

Question 2

Let $A=\begin{pmatrix}1&2\\0&1\end{pmatrix}$ and $B=\begin{pmatrix}3&0\\0&2\end{pmatrix}$. What is $BA$?

Question 3

If $T(\mathbf{x})=A\mathbf{x}$ and $S(\mathbf{x})=B\mathbf{x}$, which matrix represents $T\circ S$?

Question 4

Which property of matrix multiplication matches the fact that applying three transformations in different groupings gives the same overall result, as long as the order is unchanged?

Question 5

If $A$ is $2\times 3$ and $B$ is $3\times 4$, what is the size of $AB$?