Fill in the blank using elementary row operations to form a row-equivalent matrix. $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
- 2 & 1 & 4
\end{array} \right]$$ $\left[\begin{array}{rrr}
-1 & 5 & -3 \
0 & \square & 10
\end{array}\right]$
A) $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
0 & - 9 & 10
\end{array} \right]$$
B) $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
0 & 0 & 10
\end{array} \right]$$
C) $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
0 & 11 & 10
\end{array} \right]$$
D) $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
0 & 5 & 10
\end{array} \right]$$
E) $$\left[ \begin{array} { r r r }
- 1 & 5 & - 3 \
0 & 9 & 10
\end{array} \right]$$

Question

Fill in the blank using elementary row operations to form a row-equivalent matrix. $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
- 2 & 1 & 4
\end{array} \right]$$ $\left[\begin{array}{rrr}
-1 & 5 & -3 \
0 & \square & 10
\end{array}\right]$
A) $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
0 & - 9 & 10
\end{array} \right]$$ ​
B) $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
0 & 0 & 10
\end{array} \right]$$ ​
C) $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
0 & 11 & 10
\end{array} \right]$$ ​
D) $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
0 & 5 & 10
\end{array} \right]$$ ​
E) $$\left[ \begin{array} { r r r } 
- 1 & 5 & - 3 \
0 & 9 & 10
\end{array} \right]$$ ​

Quizplus · Accepted Answer

To eliminate the -2 in the second row, first row, we can use the operation $R_2 = R_2 + 2R_1$. Applying this to the second row gives: $-2 + 2(-1) = 0$ for the first column, $1 + 2(5) = 11$ for the second column, and $4 + 2(-3) = -2$. However, to achieve the final matrix, we actually need to subtract $2R_1$ from $R_2$, which gives $1 - 2(5) = 1 - 10 = -9$ for the second column, correctly matching option A.

Fill in the Blank Using Elementary Row Operations to Form [−15−3−214]\left[ \begin{array} { r r r } - 1 & 5 & - 3 \\- 2 & 1 & 4\end{array} \right][−1−2​51​−34​]

Fill in the Blank Using Elementary Row Operations to Form $\left[ \begin{array} { r r r } - 1 & 5 & - 3 \\- 2 & 1 & 4\end{array} \right]$