Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\text { Given } \left| \begin{array} { l l l }
\mathrm { s } & \mathrm { t } & \mathrm { u } \
\mathrm { v } & \mathrm { w } & \mathrm { x } \
4 & 2 & 8
\end{array} \right| = 3 \text {, find the value of } \left| \begin{array} { c c c }
32 - \mathrm { s } & 16 - \mathrm { t } & 64 - \mathrm { u } \
\mathrm { v } & \mathrm { w } & \mathrm { x } \
4 & 2 & 8
\end{array} \right|$$
A) -24
B) -3
C) 3
D) 24

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\text { Given } \left| \begin{array} { l l l } 
\mathrm { s } & \mathrm { t } & \mathrm { u } \
\mathrm { v } & \mathrm { w } & \mathrm { x } \
4 & 2 & 8
\end{array} \right| = 3 \text {, find the value of } \left| \begin{array} { c c c } 
32 - \mathrm { s } & 16 - \mathrm { t } & 64 - \mathrm { u } \
\mathrm { v } & \mathrm { w } & \mathrm { x } \
4 & 2 & 8
\end{array} \right|$$
A) -24
B) -3
C) 3
D) 24

Quizplus · Accepted Answer

The second determinant can be transformed into the first by adding the third row (multiplied by appropriate constants) to the first row. This operation does not change the determinant's value, so the value remains 3.

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