RREF of [[sqrt(6)/6,sqrt(3)/2,sqrt(3)/6],[-sqrt(3)/3,0,sqrt(6)/3]]

The calculator will find the reduced row echelon form of the $$$2$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}\frac{\sqrt{6}}{6} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{6}\\- \frac{\sqrt{3}}{3} & 0 & \frac{\sqrt{6}}{3}\end{array}\right]$$$, with steps shown.

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Matrix:

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Find the reduced row echelon form of $$$\left[\begin{array}{ccc}\frac{\sqrt{6}}{6} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{6}\\- \frac{\sqrt{3}}{3} & 0 & \frac{\sqrt{6}}{3}\end{array}\right]$$$.

Solution

Multiply row $$$1$$$ by $$$\sqrt{6}$$$: $$$R_{1} = \sqrt{6} R_{1}$$$.

$$$\left[\begin{array}{ccc}1 & \frac{3 \sqrt{2}}{2} & \frac{\sqrt{2}}{2}\\- \frac{\sqrt{3}}{3} & 0 & \frac{\sqrt{6}}{3}\end{array}\right]$$$

Add row $$$1$$$ multiplied by $$$\frac{\sqrt{3}}{3}$$$ to row $$$2$$$: $$$R_{2} = R_{2} + \frac{\sqrt{3}}{3} R_{1}$$$.

$$$\left[\begin{array}{ccc}1 & \frac{3 \sqrt{2}}{2} & \frac{\sqrt{2}}{2}\\0 & \frac{\sqrt{6}}{2} & \frac{\sqrt{6}}{2}\end{array}\right]$$$

Multiply row $$$2$$$ by $$$\frac{\sqrt{6}}{3}$$$: $$$R_{2} = \frac{\sqrt{6}}{3} R_{2}$$$.

$$$\left[\begin{array}{ccc}1 & \frac{3 \sqrt{2}}{2} & \frac{\sqrt{2}}{2}\\0 & 1 & 1\end{array}\right]$$$

Subtract row $$$2$$$ multiplied by $$$\frac{3 \sqrt{2}}{2}$$$ from row $$$1$$$: $$$R_{1} = R_{1} - \frac{3 \sqrt{2}}{2} R_{2}$$$.

$$$\left[\begin{array}{ccc}1 & 0 & - \sqrt{2}\\0 & 1 & 1\end{array}\right]$$$

Answer

The reduced row echelon form is $$$\left[\begin{array}{ccc}1 & 0 & - \sqrt{2}\\0 & 1 & 1\end{array}\right]\approx \left[\begin{array}{ccc}1 & 0 & -1.414213562373095\\0 & 1 & 1\end{array}\right].$$$A

RREF of $$$\left[\begin{array}{ccc}\frac{\sqrt{6}}{6} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{6}\\- \frac{\sqrt{3}}{3} & 0 & \frac{\sqrt{6}}{3}\end{array}\right]$$$

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Solution

Answer