Question

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

1 0 1-1
1 3 -1-9
3 2 0- 2
Which matrix results from the operation -3R2 R2?

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`.

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.