(sqrt(6)/2)*[[sqrt(6)/3,0],[0,sqrt(3)/3]]

The calculator will multiply the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}\frac{\sqrt{6}}{3} & 0\\0 & \frac{\sqrt{3}}{3}\end{array}\right]$$$ by the scalar $$$\frac{\sqrt{6}}{2}$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

A

Scalar:

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Your Input

Calculate $$$\frac{\sqrt{6}}{2} \left[\begin{array}{cc}\frac{\sqrt{6}}{3} & 0\\0 & \frac{\sqrt{3}}{3}\end{array}\right]$$$.

Solution

Multiply each entry of the matrix by the scalar:

$$${\color{Blue}\left(\frac{\sqrt{6}}{2}\right)}\cdot \left[\begin{array}{cc}\frac{\sqrt{6}}{3} & 0\\0 & \frac{\sqrt{3}}{3}\end{array}\right] = \left[\begin{array}{cc}{\color{Blue}\left(\frac{\sqrt{6}}{2}\right)}\cdot \left(\frac{\sqrt{6}}{3}\right) & {\color{Blue}\left(\frac{\sqrt{6}}{2}\right)}\cdot \left(0\right)\\{\color{Blue}\left(\frac{\sqrt{6}}{2}\right)}\cdot \left(0\right) & {\color{Blue}\left(\frac{\sqrt{6}}{2}\right)}\cdot \left(\frac{\sqrt{3}}{3}\right)\end{array}\right] = \left[\begin{array}{cc}1 & 0\\0 & \frac{\sqrt{2}}{2}\end{array}\right]$$$

Answer

$$$\frac{\sqrt{6}}{2} \left[\begin{array}{cc}\frac{\sqrt{6}}{3} & 0\\0 & \frac{\sqrt{3}}{3}\end{array}\right] = \left[\begin{array}{cc}1 & 0\\0 & \frac{\sqrt{2}}{2}\end{array}\right]\approx \left[\begin{array}{cc}1 & 0\\0 & 0.707106781186548\end{array}\right]$$$A

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