In this Eigenvalue and Eigenvector worksheet, students examine the applications of matrix exponentiation. This four-page worksheet provides explanations and examples, as well as three problems to complete.

In this math worksheet, students practice finding the vector spaces associated with the rectangular matrices. Then they find the complete solutions to the given equation using a matrix.

In this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...

In this identifying pivots learning exercise, students use algebra to find equivalent systems of equations. This four-page learning exercise contains examples, explanations and approximately ten problems.

In this math worksheet, students practice to find the dimensions of subspaces. They also find the solutions to the systems of equations using the matrices.

In this column space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples of and explanations. One problem is provided for students to complete.

For this projection worksheet, students determine the projections of a given matrix. This four-page worksheet contains explanations and examples and approximately ten problems to complete.

In this linear algebra worksheet, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page worksheet contains examples, explanations, and approximately four problems to complete.

In this vector spaces of a matrix instructional activity, students decompose any vector into two orthogonal pieces. They identify the nullspace, row space, and find a reduced echelon. This two-page instructional activity contains...

In this circular convolutions worksheet, students solve 8 different problems that are related to circular convolutions. They let g be defined by an arbitrary vector and determine the formula for 8 samples for f and g. Then, students find...

In this permutations worksheet, students explore a permutation matrix, symmetric matrix, and the properties of the transpose. This three-page worksheet contains six problems.

In this math worksheet, learners examine the coupled differential equations. Then they find the eigenvalues and eigenvectors for the 2x2 matrix.

In this least squares approximation instructional activity, students use linear algebra to find the least square error and the equation of a line for given points. They find the equation of a parabola through provided points. This...

In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.

In this eigenvalues worksheet, students find the eigenvalues and eigenvectors of a given matrix. This two-page worksheet contains examples, explanations and two practice problems.

Students, after reading the Drag Equation page from the NASA Web site, demonstrate an understanding of this equation and how drag is dependent on the variables included in the equation.

Learners, after reading the Drag Equation page from the NASA Web-based textbook, demonstrate an understanding of this equation and how drag is dependent on the variables included in the equation.

Students solve systems of equations. In this algebra lesson, students use matrices to solve linear equations. They use reduced row echelon-form and scalar multiplier to simplify the matrices completely.

In this computing determinants activity, learners explore methods of computing determinants. They complete determinant problems by using the co-factor method, the "big formula" and the use of product of the pivots. This two-page...

In this vector spaces and subspaces worksheet, students review column spaces of matrices. They determine if the set of all 2 by 2 matrices is a vector space. Students determine if the set of all invertible 2 by 2 matrices is a vector...

In this permutation worksheet, students multiply matrices, explore symmetric matrices, permutation matrices, and properties of the transpose. This three-page worksheet contains explanations, examples and four problems.

In this vector space matrix instructional activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page instructional activity contains examples and...

In this interpretation of eigenvalues and eigenvectors activity, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...

In this determinant worksheet, students explore the determinant of a matrix. After examining the given examples and explanations, they find the determinants of given matrices. This two-page worksheet contains nine problems.