(sqrt(2)/sqrt(3 - sqrt(5)))*[[1,0],[1,1]]

The calculator will multiply the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right]$$$ by the scalar $$$\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}$$$, with steps shown.

Size of the matrix:

$$$\times$$$

Matrix:

A

Scalar:

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Your Input

Calculate $$$\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right]$$$.

Solution

Multiply each entry of the matrix by the scalar:

$$${\color{Chocolate}\left(\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\right)}\cdot \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right] = \left[\begin{array}{cc}{\color{Chocolate}\left(\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\right)}\cdot \left(1\right) & {\color{Chocolate}\left(\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\right)}\cdot \left(0\right)\\{\color{Chocolate}\left(\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\right)}\cdot \left(1\right) & {\color{Chocolate}\left(\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\right)}\cdot \left(1\right)\end{array}\right] = \left[\begin{array}{cc}\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} & 0\\\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} & \frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\end{array}\right]$$$

Answer

$$$\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} \left[\begin{array}{cc}1 & 0\\1 & 1\end{array}\right] = \left[\begin{array}{cc}\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} & 0\\\frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}} & \frac{\sqrt{2}}{\sqrt{3 - \sqrt{5}}}\end{array}\right]\approx \left[\begin{array}{cc}1.618033988749895 & 0\\1.618033988749895 & 1.618033988749895\end{array}\right]$$$A

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