Transforming vectors with 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.

Lessons

Let column vector x be a column vector and TT be a transformation matrix. Then we can transform the column vector column vector x by multiplying it with the transformation matrix TT. In other words, transformed vector Tx is the transformed vector.
  • 1.
    Transforming vectors with matrices overview

  • 2.
    Finding the Transformed Vectors
    Apply the transformation matrix TT to the following column vector Transforming vectors with matrices to find the transformed vector:
    a)
    Transforming vectors with matrices

    b)
    Transforming vectors with matrices

    c)
    Transforming vectors with matrices

    d)
    Transforming vectors with matrices

    e)
    Transforming vectors with matrices


  • 3.
    Graphing the Transformed Vector
    Plot the column vector Transforming vectors with matrices on the graph. Then apply the transformation matrix Transforming vectors with matrices to the column vector to find the transformed vector, and plot the transformed vector on the graph.

  • 4.
    Plot the column vector Transforming vectors with matrices on the graph. Then apply the transformation matrix Transforming vectors with matrices to the column vector to find the transformed vector, and plot the transformed vector on the graph.

  • 5.
    Plot the column vector Transforming vectors with matrices on the graph. Then apply the transformation matrix Transforming vectors with matrices to the column vector to find the transformed vector, and plot the transformed vector on the graph.