Question

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

Answer 1

Answer:

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

Step-by-step 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 $\dfrac{1}{3}R_1$ and replace $R_1$ in the above matrix.

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

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

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

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