Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l }
R _ { 2 } = 5 r _ { 1 } + r _ { 2 } \
{ \left[ \begin{array} { c c | c }
1 & 6 & 11 \
- 5 & 9 & - 6
\end{array} \right] }
\end{array}$$
A) $\left[ \begin{array} { r r | r } 5 & 30 & 55 \ - 5 & 9 & - 6 \end{array} \right]$
B) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \ 0 & 39 & 49 \end{array} \right]$
C) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \ 0 & - 21 & - 61 \end{array} \right]$
D) $\left[ \begin{array} { l l | l } 5 & 30 & 55 \ 0 & 39 & 49 \end{array} \right]$

Question

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
R _ { 2 } = 5 r _ { 1 } + r _ { 2 } \
{ \left[ \begin{array} { c c | c } 
1 & 6 & 11 \
- 5 & 9 & - 6
\end{array} \right] }
\end{array}$$
A) $\left[ \begin{array} { r r | r } 5 & 30 & 55 \ - 5 & 9 & - 6 \end{array} \right]$
B) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \ 0 & 39 & 49 \end{array} \right]$
C) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \ 0 & - 21 & - 61 \end{array} \right]$
D) $\left[ \begin{array} { l l | l } 5 & 30 & 55 \ 0 & 39 & 49 \end{array} \right]$

Quizplus · Accepted Answer

To perform the row operation $R_2 = 5R_1 + R_2$, we multiply each element of $R_1$ by 5 and add it to the corresponding element of $R_2$. For the first column, $5(1) - 5 = 0$; for the second column, $5(6) + 9 = 39$; for the third column, $5(11) - 6 = 49$. This results in the new $R_2$ as shown in option B.

Perform the Row Operation(s) on the Given Augmented Matrix A) [53055−59−6]\left[ \begin{array} { r r | r } 5 & 30 & 55 \\ - 5 & 9 & - 6 \end{array} \right][5−5​309​55−6​]

Perform the Row Operation(s) on the Given Augmented Matrix A) $\left[ \begin{array} { r r | r } 5 & 30 & 55 \\ - 5 & 9 & - 6 \end{array} \right]$