Young scholars prove conjectures about geometric figures on the plane or in space using coordinate geometry. They develop fluency in operations with real numbers, vectors and matrices using mental computation or paper-and-pencil...

In this equations and inequalities review worksheet, 11th graders solve and complete 100 various types of problems. First, they solve each equation using the quadratic formula or completing the square. Then, students solve using matrices...

In this linear systems worksheet students multiply matrices and find the coefficient matrix in the upper-triangular form. This four-page worksheet contains approximately four problems, with examples and explanations.

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

In this symmetric matrices worksheet, students explore the characteristics of symmetric matrices. This two-page worksheet contains examples and explanations concerning symmetric matrices. Two problems are provided to solve.

Young mathematicians represent a triangle with a matrix and use the determinant to find the area of three given triangles. Learners also verify the formula for area of a triangle. 

In this matrix equation worksheet, students write a matrix equation for each of 3 systems. They then solve 6 matrix equations.

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 probability worksheet, students determine the probability of given events, they solve story problems using a transition matrix. This one-page worksheet contains approximately four multi-step problems.

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

For this linear systems worksheet, students find the parameter of a given matrix, and solve linear systems. This two-page worksheet contains four problems.

Start with the definition of a determinant and how to evaluate a 2x2 determinant. Apply this skill to solve systems of two equations with two unknowns by using Cramer's rule. These four basic problems would be good for a quick review or...

In this matrix inverse learning exercise, students identify a matrix which when multiplied by a coefficient matrix, it transforms into an identify matrix. They use the Gauss-Jordan elimination process to find an inverse matrix. This...

In this symmetric matrices worksheet, students find the eigenvalues of a matrix and discover that symmetric matrices are diagonalizable. This two-page worksheet contains examples, explanations and two problems.

In this rectangular matrices activity, students complete solutions to given matrices. They identify the pivot columns and examine the nullspace of a matrix. This four-page activity contains examples, explanations and approximately...

In this four matrix subspaces learning exercise, students identify statements which are always true for given matrices. Students are given five matrices and a list of ten statements.

In this Jacobian matrix worksheet, students identify the derivative matrix of a function and use the tangent approximation to approximate vectors. This two-page worksheet contains six problems.

In this differential equation worksheet, students answer seventeen problems related to first-order differential equations, vectors, systems of equations, and vector-matrix form of systems of equations.

In this projection activity, students use the Gram-Schmidt orthonormalization process to find the orthonormal basis of a matrix. They project a matrix onto the orthogonal compliment of a given plane. This two-page activity contains two...

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 linear system worksheet, students consider the linear system under given parameters. They identify the solution set of a matrix under given cases. This two-page worksheet contains three problems.

What do you get when you combine a matrix and a cube? Well that depends on the matrix! Pupils use online software to graph various transformations of a cube. Ultimately, they are able to describe the matrix that is responsible for a...

Astronomers practice downloading data from a high-energy satellite and translate the data into colored or shaded pixels. As a hands-on activity, they use pennies to simulate high-energy satellite data and they convert their penny...

Investigate the application of vector transformations applied to linear systems. Individuals use vectors to transform a linear system translating the solution to the origin. They apply their understanding of vectors, matrices,...