# Transforming vectors with matrices

##### Intros

##### Examples

###### Lessons

**Finding the Transformed Vectors**

Apply the transformation matrix $T$ to the following column vector to find the transformed vector:**Graphing the Transformed Vector**

Plot the column vector on the graph. Then apply the transformation matrix to the column vector to find the transformed vector, and plot the transformed vector on the graph.- Plot the column vector on the graph. Then apply the transformation matrix to the column vector to find the transformed vector, and plot the transformed vector on the graph.
- Plot the column vector on the graph. Then apply the transformation matrix to the column vector to find the transformed vector, and plot the transformed vector on the graph.

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###### Topic Notes

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.

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.

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