Find the determinant of the matrix. $$\left[ \begin{array} { c c c }
- 3 & 4.5 & 9 \
- 0.3 & 5.5 & 1 \
5.3 & 6.7 & 13
\end{array} \right]$$
A) -1083.6
B) -173
C) -433.44
D) -443.44

Question

Find the determinant of the matrix. $$\left[ \begin{array} { c c c } 
- 3 & 4.5 & 9 \
- 0.3 & 5.5 & 1 \
5.3 & 6.7 & 13
\end{array} \right]$$
A) -1083.6
B) -173
C) -433.44
D) -443.44

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\left[ \begin{array} { c c c } a & b & c \ d & e & f \ g & h & i \end{array} \right]$ is calculated as $a(ei - fh) - b(di - fg) + c(dh - eg)$. Applying this formula to the given matrix results in $-3(5.5 \times 13 - 1 \times 6.7) - 4.5(-0.3 \times 13 - 1 \times 5.3) + 9(-0.3 \times 6.7 - 5.5 \times 5.3)$, which simplifies to -433.44.

Find the Determinant of the Matrix [−34.59−0.35.515.36.713]\left[ \begin{array} { c c c } - 3 & 4.5 & 9 \\- 0.3 & 5.5 & 1 \\5.3 & 6.7 & 13\end{array} \right]​−3−0.35.3​4.55.56.7​9113​​

Find the Determinant of the Matrix $\left[ \begin{array} { c c c } - 3 & 4.5 & 9 \\- 0.3 & 5.5 & 1 \\5.3 & 6.7 & 13\end{array} \right]$