Matrix Teacher Resources

Example of calculating the inverse of a 2x2 matrix.

Contains explanations and examples of homogeneous transformation matrices.

Explains how simple polygons translate into matrices and how to use 2x2 matrices to represent transformations in a plane. Includes video demonstrating an example where a vector must be rotated 90 degrees using matrices. [4:18]

Match transformation matrices with a visual representation of their effect on the plane. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Find the image of a given polygon under a transformation defined by a given matrix. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Demonstrates how to represent a 2x2 matrix transformation on a plane. [6:08]

[Free Registration/Login may be required to access all resource tools.] Provides resources for working with 2 x 2 matrices as transformations of the plane, and interpreting the absolute value of the determinant in terms of area.

Figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.

Video first reviews how to find the transformation matrix using the identity matrix. Shows how to write a transformation matrix that reflects over the y-axis and scales the y-coordinates by a factor of 2. [15:13]

Students can use a graphing calculator to explore transformations with matrices. They will analyze how each element of the matrix affects the position of the image.

Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.

Video shows that the sum of two linear transformations is the sum of their transformation matrices and the scalar multiple of a transformation is the scalar multiple of the transformation matrix.

Changing our coordinate system to find the transformation matrix with respect to standard coordinates

Showing that matrix products are associative in this short video.

Video reviews what was shown in the previous video that the sum of two linear transformations is the sum of their transformation matrices and the scalar multiple of a transformation is the scalar multiple of the transformation matrix....

Video showing how to change coordinate systems to make finding the transformation matrix with respect to the standard basis easier. First, a specific linear transformation is defined and the regular method for constructing the...

Video reviewing the relationship between transformation matrices with respect to different bases. Addresses manipulating the equation to write it in terms of the transformation matrix with respect to the standard basis. The relationship...

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video shows example of multiplying matrices. Includes explanation of the dimensions needed in order for matrices to be able to be multiplied. Connects to the composition of linear transformations. This video also appears in the strand...

Video continuing the example from the previous video where a transformation matrix with respect to an alternate basis was found given a transformation matrix with respect to the standard basis, an alternate basis and a change of basis...

Video discussing transformation matrices and how a vector is able to be mapped to the same resulting vector by using a transformation matrix with respect to the standard basis as well as one with respect to a different basis. Reviews how...

Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...

Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...