Question

Perform the row operation 1/3R1 and replace R1 on the following matrix

[3 0 0|21]
[0 6 0|5]
[0 0 7|5]

Answer 1

`\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right]`

Explanation:

The given augmented matrix is

`\left[\left.\begin{matrix}3 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}21\\ 5\\ 5\end{matrix}\right]`

Here, we need to perform the row operation
`(1)/(3)R_1` and replace
`R_1` in the above matrix.

So, divide each element of
`R_1` in the given matrix and other elements remain same.

`\left[\left.\begin{matrix}(3)/(3) & (0)/(3) & (0)/(3)\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}(21)/(3)\\ 5\\ 5\end{matrix}\right]`

`\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right]`

Therefore, the required matrix is
`\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right]`.