Question

Kamal wrote the augmented matrix below to represent a system of equations

Answer 1

Consider the operation is $R_2\to -3R_2$.

Given:

The augmented matrix below represents a system of equations.

$\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right]$

To find:

Matrix results from the operation $R_2\to -3R_2$.

Step-by-step explanation:

We have,

$\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right]$

After applying $R_2\to -3R_2$, we get

$\left[\left.\begin{matrix}1&0&1\\-3(1)&-3(3)&-3(-1)\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-3(-9)\\-2\end{matrix}\right]$

$\left[\left.\begin{matrix}1&0&1\\-3&-9&3\\3&2&0\end{matrix}\right|\begin{matrix}-1\\27\\-2\end{matrix}\right]$

Therefore, the correct option is A.