1.14 Matrices Quiz

1. A $2\times3$ matrix is multiplied by a $3\times4$ matrix. What is the order of the product?

• A. $3\times3$
• B. $2\times3$
• C. $2\times4$
• D. $3\times4$

2. Find $\det\begin{pmatrix}3&1\\ 4&2\end{pmatrix}$.

• A. $2$
• B. $10$
• C. $-2$
• D. $\frac12$

3. Find the inverse of $\begin{pmatrix}3&1\\ 4&2\end{pmatrix}$.

• A. $\begin{pmatrix}2&-1\\ -4&3\end{pmatrix}$
• B. $\frac12\begin{pmatrix}3&-1\\ -4&2\end{pmatrix}$
• C. $\frac12\begin{pmatrix}2&1\\ 4&3\end{pmatrix}$
• D. $\frac12\begin{pmatrix}2&-1\\ -4&3\end{pmatrix}$

4. If $A\mathbf{x}=\mathbf{b}$ and $A$ is invertible, what is $\mathbf{x}$?

• A. $\mathbf{b}A^{-1}$
• B. $A^{-1}\mathbf{b}$
• C. $\mathbf{b}-A$
• D. $\frac{\mathbf{b}}{A}$

5. Which statement is always true when the products are defined?

• A. $AB=BA$
• B. $A+B$ is defined for any $A$ and $B$
• C. $A(B+C)=AB+AC$
• D. $AB=0$ implies $A=0$ or $B=0$