Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c }
x & y & z \
u & v & w \
1 & - 1 & 3
\end{array} \right| = - 51 \left| \begin{array} { c c c }
1 & - 1 & 3 \
2 u & 2 v & 2 w \
x - 1 & y + 1 & z - 3
\end{array} \right| = ?$$
A) $- 51$
B) $- 102$
C) 102
D) 51

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 1 & 3
\end{array} \right| = - 51 \left| \begin{array} { c c c } 
1 & - 1 & 3 \
2 u & 2 v & 2 w \
x - 1 & y + 1 & z - 3
\end{array} \right| = ?$$
A) $- 51$
B) $- 102$
C) 102
D) 51

Quizplus · Accepted Answer

The second determinant is obtained by multiplying the first row of the first determinant by $2$ and adding it to the third row. This operation does not change the value of the determinant, so the second determinant is also equal to $-51$.

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