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 activity, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page 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
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...
Curated OER
Linear Systems: Vector Spaces of a Matrix
In this vector space matrix activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page activity 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
For 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...
NASA
Space Vectors
How do you determine the position coordinates of objects in space? Using the provided worksheet, class members determine the location of the space shuttle based upon its spherical coordinates from the Dryden Flight Research Center.
EngageNY
Coordinates of Points in Space
Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation of...
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.
EngageNY
Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
Curated OER
Linear Systems: Review of Vectors
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.
Curated OER
Linear Systems: Column Space and Nullspace of a Matrix
In this matrix worksheet, students find the column space and nullspace of a matrix. They give examples of vectors. This two-page worksheet contains four problems.
EngageNY
Projecting a 3-D Object onto a 2-D Plane
Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...
EngageNY
First-Person Computer Games
How do graphic designers project three-dimensional images onto two-dimensional spaces? Scholars connect their learning of matrix transformations to graphic design. They understand how to apply matrix transformations to make...
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 instructional activity, 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
Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank activity, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
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.