Transforming vectors with matrices  Matrices
Transforming vectors with matrices
In this lesson, we will learn how to transform column vectors with matrices. To transform a vector, we need to multiply the transformation matrix with that vector. This would result in a transformed vector, where the length or direction of the vector may be changed. We will take a look at some questions which involve transforming vectors, and then graph them to notice the changes between the normal vector and the transformed vector.
Basic concepts:
 Introduction to vectors
 Notation of matrices
 Matrix multiplication
Lessons
Notes:
Let be a column vector and $T$ be a transformation matrix. Then we can transform the column vector by multiplying it with the transformation matrix $T$. In other words, is the transformed vector.

1.
Finding the Transformed Vectors
Apply the transformation matrix $T$ to the following column vector to find the transformed vector: