Curated OER
Linear Systems: Vector Spaces and Subspaces
In this vector space worksheet, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page worksheet contains approximately six multi-step problems.
Mathed Up!
Vectors
Young mathematicians connect vectors to geometric shapes by watching a video that expresses vectors in relation to the sides of geometric figures. They then apply what they learned by completing a worksheet of practice questions.
Curated OER
Introduction to Vector Spaces
In this vector spaces instructional activity, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page instructional activity contains 13 problems.
Curated OER
Linear Systems: Orthogonality of Vector Spaces of a Matrix
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.
Curated OER
Linear Systems: Vector Spaces and Subspaces
For 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...
Curated OER
Linear Systems: Vector Spaces of a Matrix
For this vector space matrix worksheet, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page worksheet contains examples and approximately five problems.
Curated OER
Linear Systems: Introduction to Vector Space
In this vector space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples, theorems, explanations, and approximately three problems.
Curated OER
Linear Systems: Vector Spaces
In this vector space worksheet, students explore linearly independent vectors. They identify the row space, null space and subspaces of a given matrix. This four-page worksheet contains approximately eight problems.
Curated OER
Linear Systems: Vector Spaces
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...
International Technology Education Association
Dampen That Drift!
The spacecraft is drifting too far off course! Two games help explain how a spacecraft can use its thrusters to maintain its position. The games have pupils be the components of vectors in order to create and counteract the disturbances.
Curated OER
Linear Systems: The Column Space
For 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.
Curated OER
Linear Systems: Review of Vectors
In this review of vectors instructional activity, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page instructional activity contains...
Curated OER
Linear Systems: Column Space and Nullspace of a Matrix
In this matrix learning exercise, students find the column space and nullspace of a matrix. They give examples of vectors. This two-page learning exercise contains four problems.
Curated OER
Linear Systems: Linear Equations, Vectors and Matrices
In this matrices worksheet, students write matrix notation to represent linear systems. This four-page worksheet contains approximately 15 problems.
Curated OER
Introduction to Linear Algebra 2.1
In this linear equation worksheet, students identify the vector space of a given matrices and find the appropriate system of equations for each of four solutions. Then they solve the system and write their conclusion.
Curated OER
Math 212: Planes
In this planes worksheet, students consider the position of given vectors and find the vector equation of a plane. They identify the points that lie on a plane and determine the equation of a line through given points. This two-page...
Mathed Up!
Translations
Introduce translations as transformations that move figures in horizontal and vertical distances with a video that shows how to translate the figures. A second video covers how to determine the translation that has occurred. Pupils work...
Curated OER
Linear Systems: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
Curated OER
Linear Systems: Projections
In this projection learning exercise, students determine the projections of a given matrix. This four-page learning exercise contains explanations and examples and approximately ten problems to complete.
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Linear Systems: Fundamental Theorem
In this fundamental theorem worksheet, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page worksheet...
Curated OER
Linear Systems: Linear Equations
In this linear systems instructional activity, students use a matrix to represent linear systems. This four page instructional activity provides examples, explanations and approximately eight problems to complete.
Curated OER
More on Least Squares
In this least squares activity, students solve 3 different problems that include determining the least squares of equations. First, they use the data given in the table to write out the normal equations a system of 2 equations in 2...
Curated OER
Linear Systems: Orthogonal Matrices
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...
Curated OER
Linear Systems
In this linear systems worksheet, 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 column...