Linear Systems: Matrix Operations

In this math worksheet, students find the solutions to the problems using the linear systems of equations. The sheet is a list of review topics.

Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse...

It is all about perspective. A video introduces the idea that the view of a vector all depends upon the perspective of the basis vectors. Knowing how to go from one coordinate system's basis vectors to another system's basis vectors...

What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...

Are all transformations of the plane linear transformations? The video provides examples of transformations of the plane and provides the definition of linear transformations. The resource begins the discussion of using matrix...

Find vectors that stay on their spans after a linear transformation. The 14th video in the series of 15 introduces the concept of eigenvectors, vectors that are only scaled during a linear transformation. The presentation illustrates the...

Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...

Bring it all to three dimensions. The short video points out that the discussion in the previous presentations in two dimensions also holds true for three dimensions. The sixth video in the series of 15 specifically makes the...

But what happens if the matrix is not square? The ninth video in a series of 15 serves as a footnote to discuss non-square matrices. The resource presents them as transformations between two and three dimensions. The presentation...

Take a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...