Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c }
x & y & z \
u & v & w \
1 & - 3 & 4
\end{array} \right| = - 138 \left| \begin{array} { c c c }
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \right| = ?$$ $$\begin{array} { c c c }
x & y & z \
a & v & w \
1 & - 3 & 4
\end{array} | = - 138 | \begin{array} { c c c }
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \mid = ?$$
A) -276
B) -138
C) 276
D) 138

Question

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & 4
\end{array} \right| = - 138 \left| \begin{array} { c c c } 
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \right| = ?$$ $$\begin{array} { c c c } 
x & y & z \
a & v & w \
1 & - 3 & 4
\end{array} | = - 138 | \begin{array} { c c c } 
x & y & z \
u & v & w \
2 & - 6 & 8
\end{array} \mid = ?$$
A) -276
B) -138
C) 276
D) 138

Quizplus · Accepted Answer

The second determinant is obtained by multiplying the third row of the first determinant by 2. The value of a determinant is scaled by the factor by which a row is scaled, so the value of the second determinant is -138 * 2 = -276.

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