Find the value of the determinant.
-$$\left| \begin{array} { r r r }
4 & 5 & - 1 \
2 & 3 & - 3 \
- 2 & 4 & 4
\end{array} \right|$$
A) 12
B) 72
C) $- 72$
D) 68

Question

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
4 & 5 & - 1 \
2 & 3 & - 3 \
- 2 & 4 & 4
\end{array} \right|$$
A) 12
B) 72
C) $- 72$
D) 68

Quizplus · Accepted Answer

The determinant of the matrix can be calculated using the formula for a 3x3 matrix: $$det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$. Substituting the values from the matrix, we get: $$det(A) = 4(3*4 - (-3)*4) - 5(2*4 - (-3)*(-2)) + (-1)(2*4 - 3*(-2))$$ = $4(12 + 12) - 5(8 - 6) - (8 + 6)$ = $4*24 - 5*2 - 14$ = $96 - 10 - 14$ = $72$.

Find the Value of the Determinant ∣45−123−3−244∣\left| \begin{array} { r r r } 4 & 5 & - 1 \\2 & 3 & - 3 \\- 2 & 4 & 4\end{array} \right|​42−2​534​−1−34​​

Find the Value of the Determinant $\left| \begin{array} { r r r } 4 & 5 & - 1 \\2 & 3 & - 3 \\- 2 & 4 & 4\end{array} \right|$