Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c }
x & y & z \
u & v & w \
1 & - 3 & - 3
\end{array} \right| = 66 \left| \begin{array} { r r r }
x & y & z \
u & v & w \
- 2 & 6 & 6
\end{array} \right| = ?$$
A) 66
B) 132
C) -66
D) -132

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & - 3
\end{array} \right| = 66 \left| \begin{array} { r r r } 
x & y & z \
u & v & w \
- 2 & 6 & 6
\end{array} \right| = ?$$
A) 66
B) 132
C) -66
D) -132

Quizplus · Accepted Answer

The second determinant can be obtained from the first by multiplying the third row by -2. The determinant of a matrix is a linear function with respect to each row. Therefore, multiplying a row by a scalar multiplies the determinant by that scalar. Since the third row of the first determinant is multiplied by -2 to get the second determinant, the value of the second determinant is -2 times the value of the first, which is -2 * 66 = -132.

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