### Vector and Matrix

##### Vector addition is given by parallelogram

Let us look at the addition of two vectors (red and blue in the picture) in **R**^{2}.
The green vector is constructed from the parallelogram.

The parallelogram tells us that the two right triangles (in gray shade) are identical.
In particular, the two pink segments of the `x`-axis have the same length. This implies that
the `x`-coordinate of the green vector is `x`_{1} + `x`_{2}.
By similar argument, the `y`-coordinate of the green vector is `y`_{1} + `y`_{2}.