Find the value of the determinant.
-$\left| \begin{array} { l l l } 5 & 4 & 3 \ 5 & 4 & 4 \ 1 & 3 & 4 \end{array} \right|$
A) $- 11$
B) 11
C) 293
D) $- 43$

Question

Quizplus · Accepted Answer

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus. For the given matrix, the determinant is calculated as follows:$$ \left| \begin{array} { l l l } 5 & 4 & 3 \ 5 & 4 & 4 \ 1 & 3 & 4 \end{array} \right| = 5(4*4 - 4*3) - 4(5*4 - 4*1) + 3(5*3 - 4*1) $$$$ = 5(16 - 12) - 4(20 - 4) + 3(15 - 4) $$$$ = 5(4) - 4(16) + 3(11) $$$$ = 20 - 64 + 33 $$$$ = -11 $$Therefore, the value of the determinant is $-11$.

Find the Value of the Determinant ∣543544134∣\left| \begin{array} { l l l } 5 & 4 & 3 \\ 5 & 4 & 4 \\ 1 & 3 & 4 \end{array} \right|​551​443​344​​

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