Eigenvalues, Eigenvectors, and Diagonalization

In this "Eigenvalues and Eigenvectors" worksheet, learners find the eigenvalue of a matrix and explore the properties of eigenvalues with a matrix. This two page worksheet contains two multi-step problems.

For this math worksheet, students practice finding the Eigenvalues and Eigenvectors. They find the special factors of the given matrices.

in this math activity, students practice finding the determinant for each matrix. Then they use the solutions to develop a hypothesis for the determinants.

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...

Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain 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...

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...

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...

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...

In this eigenvalues and eigenvectors worksheet, students determine eigenvalues and eigenvectors for twenty-two problems.  Students write two poofs on this worksheet.