Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l }
R _ { 2 } = - 2 r _ { 2 } + r \
{ \left[ \begin{array} { r r r | r }
2 & 4 & 6 & - 8 \
1 & 2 & 3 & 6 \
4 & 6 & 7 & 1
\end{array} \right] }
\end{array}$$

A) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$

C) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & 0 \ 4 & 6 & 7 & 1 \end{array} \right]$

D) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & 6 \ 4 & 6 & 7 & 1 \end{array} \right]$

Question

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
R _ { 2 } = - 2 r _ { 2 } + r \
{ \left[ \begin{array} { r r r | r } 
2 & 4 & 6 & - 8 \
1 & 2 & 3 & 6 \
4 & 6 & 7 & 1
\end{array} \right] }
\end{array}$$

A) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$

B) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$

C) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & 0 \ 4 & 6 & 7 & 1 \end{array} \right]$

D) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & 6 \ 4 & 6 & 7 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The operation $R_2 = -2R_2 + R_1$ applied to the second row of the matrix involves multiplying the second row by -2 and then adding the first row to it. This results in the second row becoming $0, 0, 0, -20$, as shown in option A.

Perform the Row Operation(s) on the Given Augmented Matrix A) [246−8000−204671]\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]​204​406​607​−8−201​​

Perform the Row Operation(s) on the Given Augmented Matrix A) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]$