Rotates a vector by degrees counter-clockwise.
Projects a vector onto the - plane (the component becomes 0).
The point of showing these matrices is that there are ways to think about multiplying vectors by matrices outside the context of linear systems of equations. (These matrices aren’t always in row-reduced form.)
These can be thought of as functions (for every input there is one output) with special properties.
(This third property shows that the function has a fixed origin, and is a result of the first property.)
We call any function with these properties a linear transformation, even if it’s not a matrix.
For all in , is a linear transformation.
If , then is called a contraction.
If , then is called a dialation.
If is a matrix, then is a linear transformation from to .