Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { r r r }
\mathrm { x } & \mathrm { y } & \mathrm { z } \
\mathrm { u } & \mathrm { v } & \mathrm { w } \
1 & - 2 & - 4
\end{array} \right| = 119 \left| \begin{array} { c c c }
1 & - 2 & - 4 \
\mathrm { u } & \mathrm { v } & \mathrm { w } \
\mathrm { x } & \mathrm { y } & \mathrm { z }
\end{array} \right| = ?$$
A) 119
B) $- 119$
C) 0
D) Cannot determine

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { r r r } 
\mathrm { x } & \mathrm { y } & \mathrm { z } \
\mathrm { u } & \mathrm { v } & \mathrm { w } \
1 & - 2 & - 4
\end{array} \right| = 119 \left| \begin{array} { c c c } 
1 & - 2 & - 4 \
\mathrm { u } & \mathrm { v } & \mathrm { w } \
\mathrm { x } & \mathrm { y } & \mathrm { z }
\end{array} \right| = ?$$
A) 119
B) $- 119$
C) 0
D) Cannot determine

Quizplus · Accepted Answer

Swapping two rows of a determinant changes its sign. The second determinant is obtained by swapping the first and third rows of the first, thus its value is $-119$.

Use the Properties of Determinants to Find the Value of the Second