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

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

In this linear system activity, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page activity contains approximately seven problems.

In this nullspace matrix activity, students observe the rank and number of independent rows and columns a matrix has. They compute the product of matrices and describe the column space of each. This two-page activity contains...

In this orthogonal matrices learning exercise, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page learning exercise contains...

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

In this linear systems learning exercise, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the...

In this review of vectors worksheet, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page worksheet contains approximately ten problems.

In this multiplication of vectors worksheet, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm...

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

In this linear systems worksheet, students use a matrix to represent linear systems. This four page worksheet provides examples, explanations and approximately eight problems to complete.

In this matrices worksheet, students write matrix notation to represent linear systems. This four-page worksheet contains approximately 15 problems.

In this pivot learning exercise, students explore the elimination process, and write a matrix in upper triangular form. They identify equivalent systems. This four-page learning exercise contains examples, explanations, and...

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

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 determinant worksheet, students explore the properties of the determinant. They compute determinants by using the co-factor method, the "big formula" and the product of pivots. This two-page worksheet contains explanations,...

In this diagonalizing a matrix worksheet, students explore matrix factorization and use diagonal decomposition. This two-page worksheet contains examples, explanations and four practice problems.

In this math worksheet, students practice reviewing the different method to find the inverse for a matrix. They compute the determinant of a matrix.

In this elimination worksheet, students use the elimination process to transform a system into an equivalent form. This three-page worksheet contains three practice problems as well as examples and explanations.

In this math instructional activity, learners examine the process of multiplying vectors to find their products. They practice finding the geometric and algebraic views for the solutions.

In this vector and matrix learning exercise, students explore matrix notation to represent linear systems. They use geometric interpretations of linear systems. This three-page learning exercise contains three practice problems,...

In this math instructional activity, learners find the values by factoring a matrix A into the product of a lower triangular matrix L. They also make it into an upper matrix U.

In this math worksheet, students investigate using the accumulation method to solve for the functions. They also review using Riemann Sums.