Fill in the blank using elementary row operations to form a row-equivalent matrix.
$$\begin{array} { l }
{ \left[ \begin{array} { c c c }
2 & - 1 & - 9 \
8 & - 6 & 4
\end{array} \right] } \
{ \left[ \begin{array} { c c c }
2 & - 1 & - 9 \
0 & \square & 40
\end{array} \right] }
\end{array}$$
A) $\left[ \begin{array} { r r r } 2 & - 1 & - 9 \ 0 & - 2 & 40 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & 0 & 40 \end{array} \right]$
C) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & - 10 & 40 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 2 & - 1 & - 9 \ 0 & - 1 & 40 \end{array} \right]$
E) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & 2 & 40 \end{array} \right]$

Question

Fill in the blank using elementary row operations to form a row-equivalent matrix.
$$\begin{array} { l } 
{ \left[ \begin{array} { c c c } 
2 & - 1 & - 9 \
8 & - 6 & 4
\end{array} \right] } \
{ \left[ \begin{array} { c c c } 
2 & - 1 & - 9 \
0 & \square & 40
\end{array} \right] }
\end{array}$$
A) $\left[ \begin{array} { r r r } 2 & - 1 & - 9 \ 0 & - 2 & 40 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & 0 & 40 \end{array} \right]$
C) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & - 10 & 40 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 2 & - 1 & - 9 \ 0 & - 1 & 40 \end{array} \right]$
E) $\left[ \begin{array} { c c c } 2 & - 1 & - 9 \ 0 & 2 & 40 \end{array} \right]$

Quizplus · Accepted Answer

To eliminate the $8$ in the second row, first row, we can use the operation $R_2 - 4R_1 \rightarrow R_2$. Applying this to the second element in the row gives $-6 - 4(-1) = -6 + 4 = -2$, which matches option A.

Fill in the Blank Using Elementary Row Operations to Form