|
|
|
|
|
|
|
|
|
|
|
|
RREF of $$$\left[\begin{array}{cc}\frac{1}{5} & \frac{1}{5}\\\frac{1}{5} & \frac{1}{5}\end{array}\right]$$$
Related calculators: Gauss-Jordan Elimination Calculator, Matrix Inverse Calculator
Your Input
Find the reduced row echelon form of $$$\left[\begin{array}{cc}\frac{1}{5} & \frac{1}{5}\\\frac{1}{5} & \frac{1}{5}\end{array}\right]$$$.
Solution
Multiply row $$$1$$$ by $$$5$$$: $$$R_{1} = 5 R_{1}$$$.
$$$\left[\begin{array}{cc}1 & 1\\\frac{1}{5} & \frac{1}{5}\end{array}\right]$$$
Subtract row $$$1$$$ multiplied by $$$\frac{1}{5}$$$ from row $$$2$$$: $$$R_{2} = R_{2} - \frac{R_{1}}{5}$$$.
$$$\left[\begin{array}{cc}1 & 1\\0 & 0\end{array}\right]$$$
Since the element at row $$$2$$$ and column $$$2$$$ (pivot element) equals $$$0$$$, we need to swap the rows.
Find the first nonzero element in column $$$2$$$ under the pivot entry.
As can be seen, there are no such entries.
Answer
The reduced row echelon form is $$$\left[\begin{array}{cc}1 & 1\\0 & 0\end{array}\right]$$$A.