Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c }
x & y & z \
u & v & w \
1 & - 3 & - 4
\end{array} \right| = 62 \left| \begin{array} { c c c }
1 & - 3 & - 4 \
3 u & 3 v & 3 w \
x - 1 & y + 3 & z + 4
\end{array} \right| = ?$$
A) 186
B) -186
C) 62
D) -62

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & - 4
\end{array} \right| = 62 \left| \begin{array} { c c c } 
1 & - 3 & - 4 \
3 u & 3 v & 3 w \
x - 1 & y + 3 & z + 4
\end{array} \right| = ?$$
A) 186
B) -186
C) 62
D) -62

Quizplus · Accepted Answer

The second determinant can be obtained by performing row operations on the first determinant. Specifically, the second determinant is obtained by multiplying the second row of the first determinant by 3 and then swapping the first and third rows. Swapping rows changes the sign of the determinant, and multiplying a row by a scalar multiplies the determinant by that scalar. Therefore, the value of the second determinant is -3 times the value of the first determinant, which is -3 * 62 = -186.

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