In this section, we will be focusing on finding the transformation matrix.
Given a picture or a description of the transformation, how do we find the transformation matrix? What we do is to take a look at the two unit vectors:
We want to ask ourselves how the transformation given in the question changes these two unit vectors.
Let's say that the unit vector
and the unit vector
. Then we say that:
Then we combine these two column vectors into one matrix.
Hence, the transformation matrix is: