3x3 determinants and inverse matrices Quiz

1. Find $\det\begin{pmatrix}1&0&2\\0&3&1\\0&0&2\end{pmatrix}$.

• A. $6$
• B. $5$
• C. $3$
• D. $2$

2. A $2\times2$ transformation matrix has determinant $-3$. Which statement is true?

• A. Areas are multiplied by $-3$
• B. Areas are multiplied by $\frac13$ and orientation is preserved
• C. Areas are multiplied by $3$ and orientation is preserved
• D. Areas are multiplied by $3$ and orientation is reversed

3. In a $3\times3$ expansion, the cofactor of the entry in row 1, column 2 is the minor multiplied by which factor?

• A. $+1$
• B. $-1$
• C. $2$
• D. $0$

4. A $3\times3$ matrix has determinant $4$. A solid of volume $5\text{ cm}^3$ is transformed by it. What is the image volume?

• A. $9\text{ cm}^3$
• B. $1.25\text{ cm}^3$
• C. $20\text{ cm}^3$
• D. $-20\text{ cm}^3$

5. For which value of $k$ is $\begin{pmatrix}1&2&3\\4&5&6\\7&8&k\end{pmatrix}$ singular?

• A. $k=9$
• B. $k=7$
• C. $k=8$
• D. $k=3$