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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?
The existence of the lake is practically as recent as the discovery of the lake. The discovery was made in 2018 by local hikers, who made the journey to the lake’s beach. The depth of the water is extremely low, and the explorers found out that it is possible to walk on the lake surface for about one kilometer in each direction. The crystalline water was created as a result of rainfall, which flowed from the mountain. The lake is connected with the sea through a narrow channel on the coast of the lake. Because the lake is a shallow lake, it is difficult to assess its volume. However, scientists believe that the volume of water in the lake is close to the volume of lakes which exist in Africa.Q:
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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