Evaluate $3 \times 3$ determinant. $$\left| \begin{array} { c c c }
5 & - 7 & - 4 \
8 & - 4 & 3 \
3 & 0 & 0
\end{array} \right|$$ Use the properties of determinants to your advantage.
A) -23
B) -167
C) 15

Question

Evaluate $3 \times 3$ determinant. $$\left| \begin{array} { c c c } 
5 & - 7 & - 4 \
8 & - 4 & 3 \
3 & 0 & 0
\end{array} \right|$$ Use the properties of determinants to your advantage.
A) -23
B) -167
C) 15

Quizplus · Accepted Answer

We can expand this determinant using minors along the first row. Doing so, we get:
$$\left| \begin{array} { c c c } 
5 & - 7 & - 4 \
8 & - 4 & 3 \
3 & 0 & 0
\end{array} \right| = 5 \cdot \left| \begin{array} { c c } 
- 4 & 3 \
0 & 0
\end{array} \right| -7 \cdot \left| \begin{array} { c c } 
8 & 3 \
0 & 0
\end{array} \right| -4 \cdot \left| \begin{array} { c c } 
8 & -4 \
3 & 0
\end{array} \right|$$
Simplifying the minors, we get:
$$\left| \begin{array} { c c c } 
5 & - 7 & - 4 \
8 & - 4 & 3 \
3 & 0 & 0
\end{array} \right| = -20\cdot 5 - 0 + 12\cdot 4 = -100 + 48 = \boxed{-52}$$
Therefore, none of the answer choices are correct.

Evaluate 3×33 \times 33×3 Determinant ∣5−7−48−43300∣\left| \begin{array} { c c c } 5 & - 7 & - 4 \\8 & - 4 & 3 \\3 & 0 & 0\end{array} \right|​583​−7−40​−430​​

Evaluate $3 \times 3$ Determinant $\left| \begin{array} { c c c } 5 & - 7 & - 4 \\8 & - 4 & 3 \\3 & 0 & 0\end{array} \right|$