Use the properties of determinants to find the value of the second determinant, given the value of the first.
-Given $\left| \begin{array} { l l l } \mathrm { s } & \mathrm { t } & \mathrm { u } \ \mathrm { v } & \mathrm { w } & \mathrm { x } \ 4 & 2 & 8 \end{array} \right| = 3$, 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

Quizplus · Accepted Answer

The determinant of a matrix is a special number that can be calculated from its elements. In this case, the second determinant can be found by applying properties of determinants related to adding or subtracting rows or columns. Specifically, subtracting each element in the third row of the first determinant from the corresponding element in the first row gives the first row of the second determinant. This operation does not change the value of the determinant. Therefore, the value of the second determinant is the same as the first, which is 3.

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