Perform the matrix row operation (or operations)and write the new matrix.
-$\left[ \begin{array} { r r r | r } 1 & - 4 & 1 & 3 \ - 5 & 0 & 3 & - 3 \ - 1 & 2 & - 2 & - 1 \end{array} \right] - 3 R _ { 1 } + R _ { 2 }$

A)$ \left[\begin{array}{rrr|r}1 & -4 & 1 & 3 \ -8 & 12 & 0 & -12 \ -1 & 2 & -2 & -1\end{array}\right] $

B)$ \left[\begin{array}{ccc|c}1 & -4 & 1 & 3 \ -2 & -12 & 6 & 6 \ -1 & 2 & -2 & -1\end{array}\right] $

C)$ \left[\begin{array}{rrr|r}16 & -4 & -8 & 12 \ -5 & 0 & 3 & -3 \ -1 & 2 & -2 & -1\end{array}\right] $

D)$ \left[\begin{array}{ccc|c}-8 & 12 & 0 & -12 \ -5 & 0 & 3 & -3 \ -1 & 2 & -2 & -1\end{array}\right] $

Question

Perform the matrix row operation (or operations)and write the new matrix.
-$\left[ \begin{array} { r r r | r } 1 & - 4 & 1 & 3 \ - 5 & 0 & 3 & - 3 \ - 1 & 2 & - 2 & - 1 \end{array} \right] - 3 R _ { 1 } + R _ { 2 }$

A)$ \left[\begin{array}{rrr|r}1 & -4 & 1 & 3 \ -8 & 12 & 0 & -12 \ -1 & 2 & -2 & -1\end{array}\right] $
 
B)$ \left[\begin{array}{ccc|c}1 & -4 & 1 & 3 \ -2 & -12 & 6 & 6 \ -1 & 2 & -2 & -1\end{array}\right] $

C)$ \left[\begin{array}{rrr|r}16 & -4 & -8 & 12 \ -5 & 0 & 3 & -3 \ -1 & 2 & -2 & -1\end{array}\right] $

D)$ \left[\begin{array}{ccc|c}-8 & 12 & 0 & -12 \ -5 & 0 & 3 & -3 \ -1 & 2 & -2 & -1\end{array}\right] $

Quizplus · Accepted Answer

To perform the operation $ -3 R_1 + R_2 $, multiply each element of row 1 by -3 and add it to the corresponding element of row 2. This results in the new row 2: $(-3*1 + -5) = -8$, $(-3*-4 + 0) = 12$, $(-3*1 + 3) = 0$, $(-3*3 + -3) = -12$. The rest of the matrix remains unchanged.