sqrt(3)*[[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 $$$\sqrt{3}$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

A

Scalar:

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Your Input

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

Solution

Multiply each entry of the matrix by the scalar:

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

Answer

$$$\sqrt{3} \left[\begin{array}{cc}\frac{\sqrt{6}}{3} & 0\\0 & \frac{\sqrt{3}}{3}\end{array}\right] = \left[\begin{array}{cc}\sqrt{2} & 0\\0 & 1\end{array}\right]\approx \left[\begin{array}{cc}1.414213562373095 & 0\\0 & 1\end{array}\right]$$$A

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