Matrix Teacher Resources

Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations. Relates vector transformations to video game graphics. This video...

Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations. Relates vector transformations to video game graphics. This video...

Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends...

A video lesson working another example for finding the projection of an arbitrary vector onto a specific subspace in R3. The basis of the subspace is a 3 x 2 matrix. Uses an alternate method for find the transformation matrix that...

Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...

Video first defines the sum of transformations. Shows that the sum of two transformations is equal to the sum of their transformation matrices. Defines scalar multiples of linear transformations and shows that they are equal to the...

Video shows that the transformation matrix of the composition of linear functions is the product of the transformation matrices of each linear transformation in the composition. [16:30]

An instructional video that works through a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace. Matrix operations are used along with the...

Video lesson about how orthogonal matrices preserve lengths and angles of vectors when multiplied. Preservation of lengths is shown by manipulating the length of the square of an orthogonal matrix times a vector and preservation of...

A video lesson proving that any projection onto a subspace is actually a linear transformation. Also, if given the basis for the subspace then the specific transformation matrix for the projection can be found. Includes a brief...

Discover how to use a translation matrix to translate a figure on the coordinate plane. [6:25]

[Free Registration/Login Required] This is a lesson on transforming, rotating and dilating matrices.

Find the result (both algebraically and graphically) of transforming a vector using a transformation matrix. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

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.

Example of finding the transformation matrix for an alternate basis.

Examples, solutions, videos, and lessons to help students learn how to multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of...

This interactive applet allows you to manipulate polygons using matrices.

Math World offers the transformational matrix that allows us to rotate a two dimensional coordinate which in turn rotates the image. The page also offers the transformational matrix for rotation in three dimensions.

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 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....

Providing the motivation for definition of matrix products in this short video.

Video first defines the sum of transformations. Shows that the sum of two transformations is equal to the sum of their transformation matrices. Defines scalar multiples of linear transformations and shows that they are equal to the...

Video shows that the transformation matrix of the composition of linear functions is the product of the transformation matrices of each linear transformation in the composition. [16:30]

Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations.