Find the value of the determinant.
-$$\left| \begin{array} { l l l }
4 & 4 & 5 \
1 & 0 & 2 \
2 & 1 & 5
\end{array} \right|$$
A) 7
B) 49
C) $- 7$
D) $- 39$

Question

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
4 & 4 & 5 \
1 & 0 & 2 \
2 & 1 & 5
\end{array} \right|$$
A) 7
B) 49
C) $- 7$
D) $- 39$

Quizplus · Accepted Answer

The determinant of a 3x3 matrix $\begin{vmatrix} a & b & c \ d & e & f \ g & h & i \end{vmatrix}$ is calculated as $a(ei-fh) - b(di-fg) + c(dh-eg)$. Applying this to the given matrix, we get $4(0*5 - 2*1) - 4(1*5 - 2*2) + 5(1*1 - 0*2) = 4(0 - 2) - 4(5 - 4) + 5(1) = -8 - 4 + 5 = -7$.

Find the Value of the Determinant ∣445102215∣\left| \begin{array} { l l l } 4 & 4 & 5 \\1 & 0 & 2 \\2 & 1 & 5\end{array} \right|​412​401​525​​

Find the Value of the Determinant $\left| \begin{array} { l l l } 4 & 4 & 5 \\1 & 0 & 2 \\2 & 1 & 5\end{array} \right|$