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

Encuentre la forma escalonada por filas reducida de $$$\left[\begin{array}{ccc}\frac{\sqrt{6}}{6} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{6}\\- \frac{\sqrt{3}}{3} & 0 & \frac{\sqrt{6}}{3}\end{array}\right]$$$.

Multiplique la fila $$$1$$$ por $$$\sqrt{6}$$$: $$$R_{1} = \sqrt{6} R_{1}$$$.

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

Agregue la fila $$$1$$$ multiplicada por $$$\frac{\sqrt{3}}{3}$$$ a la fila $$$2$$$: $$$R_{2} = R_{2} + \frac{\sqrt{3}}{3} R_{1}$$$.

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

Multiplique la fila $$$2$$$ por $$$\frac{\sqrt{6}}{3}$$$: $$$R_{2} = \frac{\sqrt{6}}{3} R_{2}$$$.

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

Reste la fila $$$2$$$ multiplicada por $$$\frac{3 \sqrt{2}}{2}$$$ de la fila $$$1$$$: $$$R_{1} = R_{1} - \frac{3 \sqrt{2}}{2} R_{2}$$$.

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

La forma escalonada de fila reducida es $$$\left[\begin{array}{ccc}1 & 0 & - \sqrt{2}\\0 & 1 & 1\end{array}\right]\approx \left[\begin{array}{ccc}1 & 0 & -1.414213562373095\\0 & 1 & 1\end{array}\right].$$$A