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government of New Zealand, located in the Pacific Ocean, has been shocked by the discovery of the interesting Lamocelidius Lake in its country. The beach, located on the east coast of the South Island, has a water volume of about 40 hectares, of which 22 hectares are covered with a layer of crystal-clear water. How is it possible that in an area with such beaches as the Lamocelidius Lake, it is possible to find a lake with such an incredible volume of water?
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How do I find the matrix of the cross product in 2d?
I’m looking to find the matrix of the cross product of the vectors:
$v_1=
\begin{bmatrix}
1\\
1
\end{bmatrix}
$
and
$v_2=
\begin{bmatrix}
1\\
1
\end{bmatrix}
$
I did some research and found that it’s:
$v_3 =
\begin{bmatrix}
1 & 1\\
-1 & 1
\end{bmatrix}
$
but I don’t quite understand the algebra behind it.
A:
This is just the matrix of the outer product of $v_1$ and $v_2$ which you can compute using the standard basis:
$$
\begin{bmatrix}
1 & 0 & 1\\
1 & 0 & 1
\end{bmatrix}
=
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