EngageNY
Linear Transformations as Matrices
Don't stop with two-dimensional learning, go to the next dimension! Learners verify that 3x3 matrices represent linear transformations in the third dimension. Additionally, they verify the algebraic properties that extend to vector...
EngageNY
Solving Equations Involving Linear Transformations of the Coordinate Space
Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application questions...
Curated OER
Let the Matrix Do It
Students create a matrix of the vertices of a triangle and produce new matrices that dilate, translate, rotate, and reflect the original triangle. After multiplying each matrix by a new scale factor, they graph the new matrix and...
Curated OER
Matrices and Transformations
For this matrix worksheet, learners explore and solve problems with matrices by addition, subtraction, multiplication and using linear equations. There are 28 problems with some answers.
Curated OER
2D Wavelet Transform
In this 2D wavelet transform worksheet, students compute 9 different types of problems related to using wavelets. They select a set of orthogonal filters, load in any image they want, and compute by the given command. Then, students...
Curated OER
Transformations Using Matrices
In this transformations worksheet, 10th graders solve and complete 16 different types of problems. First, they graph the image of the figure using the transformation given. Then, students find the coordinates of the vertices of each...
EngageNY
Why Are Vectors Useful? 2
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,...
Curated OER
Linear Systems: The Inverse Matrix
In this inverse matrix worksheet, students find the product of matrices. They generate an inverse matrix using the Gauss-Jordan elimination method. This two-page worksheet contains explanations, examples and two practice problems.
EngageNY
Linear Transformations Applied to Cubes
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...
EngageNY
Mid-Module Assessment Task: Pre-Calculus Module 2
Assess your classes' knowledge using questions that require high-level thinking and explanation. Learners use matrices to answer application questions. They also demonstrate their understanding of matrix operations.
Curated OER
Eigenvalues, Eigenvectors, and Diagonalization
Students determine eigenvectors and eigenvalues for a matrix. Students diagonalize a matrix. Similar matrices are defined. Determinant formula is given for an degree n polynomial.
EngageNY
The Hunt for Better Notation
The matrix — it's not just a movie. The lesson introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as matrix multiplication...
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...
IMSA
Geometric Transformations with Matrices
In this math worksheet, learners find the values associated with the geometric transformations. They read the instruction sheet for completing matrices with translations, rotations, reflections, and scaling by adding and multiplying...
Curated OER
Linear Algebra
In this linear algebra worksheet, students solve 3 different sets of problems that include rank, dimension, nullspace and range of linear algebra. They determine the relation between the rank of a matrix and the dimension of its range....
Curated OER
Linear Systems: Matrix Inverse
In this linear systems activity students multiply matrices and find the coefficient matrix in the upper-triangular form. This four-page activity contains approximately four problems, with examples and explanations.
Curated OER
Transformers
Students use transformation to move the graph around. In this geometry lesson, students observe transformation of symmetry groups. They use the TI to move the sides of the polygons around and make predictions.
EngageNY
End-of-Module Assessment Task — Precalculus (Module 1)
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
EngageNY
Designing Your Own Game
Your classes become video game designers for a day! They utilize their matrices, vectors, and transformation skills to create and design their own game images. The complex task requires learners to apply multiple concepts to create their...
EngageNY
Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
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...
EngageNY
Introduction to Networks
Watch as matrices break networks down into rows and columns! Individuals learn how a network can be represented as a matrix. They also identify the notation of matrices.
Curated OER
Linear Systems: The Matrix Inverse
In this matrix inverse instructional activity, 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. ...
EngageNY
The Geometric Effect of Multiplying by a Reciprocal
Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...