CK-12 Foundation
Multiplying Matrices by a Scalar: Column Vectors
Make connections between vectors and matrices through multiplication. Scholars use the interactive to view the effect of multiplying a matrix by a scalar. The interactive displays the resulting matrix and its corresponding column vectors...
Center for Innovation in Mathematics Teaching
Vectors
Investigate vectors and learn how to use them. Explore why size and direction, as well as knowing speed and distance, are important components of the vector problems you are trying to solve. This is an extensive lesson which includes six...
EngageNY
Vectors in the Coordinate Plane
Examine the meaning and purpose of vectors. Use the instructional activity to teach your classes how find the magnitude of a vector and what it represents graphically. Your pupils will also combine vectors to find a resultant vector and...
Corbett Maths
Transformations: Translations
Slide into vector transformations. Column vectors define the translation of figures by defining the number of units to move horizontally and vertically on the coordinate graph. Pupils develop an understanding of how to read the...
EngageNY
Complex Numbers as Vectors
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
Physics Classroom
Component Addition
Learn to analyze vector addition on graph paper through multiple levels of practice problems. Pupils begin with two component addition and move through three and four components to prove mastery as one part of a series on vectors and...
Curated OER
Vector Manipulation Unit
Students are introduced to the concept/idea of a vector, what it represents and why they are used. They develop an understanding of what vectors are, how and why they are used.
Curated OER
Linear Systems: Review of Vectors
For 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
Introduction to Vector Spaces
In this vector spaces learning exercise, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page learning exercise 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
Matrices and Vectors
In this matrices and vectors worksheet, students solve 9 various types of problems related to forming matrices and vectors. First, they set up each system of equations listed in matrix form using mathematical notation. Then, students...
Curated OER
Linear Systems: The Column Space
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.
Curated OER
Linear Systems: Vector Spaces and Subspaces
In this vector space learning exercise, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page learning exercise contains approximately six multi-step...
Curated OER
Solution Sets and Linear Independence of Vectors
Eleventh graders study homogeneous linear systems. In this linear system of equations lesson, 11th graders write linear system solutions in parametric vector form. Students also identify the connection between linear independence and...
Curated OER
Genetic Technology
In this genetic worksheet, students will match 6 terms associated with gene engineering to their correct definition. Then students will complete a table indicating if the vector is mechanical or biological. Finally, students will...
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: 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.
EngageNY
End-of-Module Assessment Task: Pre-Calculus Module 2
Assess pupil understanding of the relationship between matrices, vectors, linear transformations, and parametric equations. Questions range from recall to more complex levels of thinking. Problems represent topics learned throughout the...
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.
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
Translation
Tenth graders identify and interpret vocabulary terms as they relate to vectors. Students practice translations by creating several tessellations. Students determine the direction and distance using vectors. Students use grid paper to...
Curated OER
Introduction to Linear Algebra 1.3
In this linear algebra activity, students write down the system that arises from the vector equation stated. Then they apply the Gaussian elimination method to solve their system. Finally, students explain their conclusion and answer the...
Curated OER
Least Squares
For this least squares worksheet, students solve 6 different problems that include the least squares of numbers. First, they plot 3 points on the axes shown and draw in their best approximating line. Then, students estimate the slope and...
Curated OER
Linear Systems: Vector Spaces
For 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...