# 2D Scalar Matrix

In this example, the matrix is a two by two matrix that takes 2D vector as input and produced a scaled 2D vector as output.

The first step to applying the matrix to an input vector is to set up the system of equations.

Let’s input a test vector and solve for the ouput vector .

Visually the input and output of the matrix can be visualized in two-dimensional space.

Finally, we can write the shorthand notation and confirm that the green vector has been scaled by a factor of two, resulting in a blue ouput vector .