Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$\left| \begin{array} { r r r } x & y & z \ u & v & w \ 1 & - 2 & 3 \end{array} \right| = 22 \left| \begin{array} { c c c } x & y & z - x \ u & v & w - u \ 1 & - 2 & 2 \end{array} \right| = ?$
A) 0
B) $- 22$
C) 22
D) Cannot determine

Question

Quizplus · Accepted Answer

The second determinant can be simplified by adding the first column to the third column, which does not change its value due to the properties of determinants. This operation reverts the third column of the second determinant to its original form in the first determinant, making the two determinants identical. Therefore, the value of the second determinant is also 22.

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