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Lesson Plan
EngageNY

When Can We Reverse a Transformation? 3

For Teachers 11th - 12th Standards
When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third lesson on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two lessons....
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Instructional Video12:09
1
1
3Blue1Brown

Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6

For Students 11th - Higher Ed Standards
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse...
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Lesson Plan
EngageNY

Representing Reflections with Transformations

For Teachers 11th - 12th Standards
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
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Lesson Plan
EngageNY

First-Person Computer Games

For Teachers 11th - 12th Standards
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...
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Lesson Plan
Curated OER

Exploring Transformations with Matrices

For Teachers 9th - 12th Standards
A page right out of the Holt Geometry book. Use a graphing calculator and graph paper to explore transformations with matrices.  
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Lesson Plan
Curated OER

Matrices: A Secret Weapon

For Teachers 9th - 11th
Students perform operations with matrices. In this algebra lesson, students use cryptography and cryptanalysis to solve problems. They add, subtract, and multiply matrices.
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Unit Plan
EngageNY

Complex Numbers and Transformations

For Teachers 11th - 12th Standards
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
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Lesson Plan
EngageNY

Matrix Multiplication Is Distributive and Associative

For Teachers 11th - 12th Standards
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson in the series, pupils now test the associative and distributive properties. The...
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Lesson Plan
1
1
EngageNY

Solving Equations Involving Linear Transformations of the Coordinate Plane

For Teachers 11th - 12th Standards
How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...
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Lesson Plan
EngageNY

Linear Transformations as Matrices

For Teachers 11th - 12th Standards
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...
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Lesson Plan
1
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EngageNY

Solving Equations Involving Linear Transformations of the Coordinate Space

For Teachers 11th - 12th Standards
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...
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Lesson Plan
Curated OER

Let the Matrix Do It

For Teachers 7th - 8th
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...
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Worksheet
Curated OER

Matrices and Transformations

For Students 10th - 12th Standards
In 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.
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Worksheet
Curated OER

2D Wavelet Transform

For Students 12th - Higher Ed
In this 2D wavelet transform instructional activity, 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,...
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Lesson Plan
Curated OER

Dilations with Matrices

For Teachers 9th - 12th Standards
Math whizzes explore dilations. They use matrices to perform dilations centered at the origins of triangles and investigate the effect of scale factor on the size relationship between the pre-image and the image of a polygon. A link to...
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Worksheet
Curated OER

Transformations Using Matrices

For Students 10th
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...
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Lesson Plan
EngageNY

Why Are Vectors Useful? 2

For Teachers 11th - 12th Standards
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,...
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Instructional Video13:10
1
1
3Blue1Brown

Cross Products in the Light of Linear Transformations | Essence of Linear Algebra Chapter 8 Part 2

For Students 11th - Higher Ed Standards
What do cross products and parallelpipeds have in common? The video discusses the geometric representation of the cross product. The geometric interpretation explains why the computational trick in calculating the cross product works.
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Worksheet
Curated OER

Linear Systems: The Inverse Matrix

For Students Higher Ed
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.
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Lesson Plan
EngageNY

Linear Transformations Applied to Cubes

For Teachers 11th - 12th Standards
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...
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Assessment
EngageNY

Mid-Module Assessment Task: Pre-Calculus Module 2

For Students 11th - 12th Standards
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.
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Lesson Plan
Curated OER

Eigenvalues, Eigenvectors, and Diagonalization

For Teachers Higher Ed
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.
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Lesson Plan
EngageNY

The Hunt for Better Notation

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Projecting a 3-D Object onto a 2-D Plane

For Teachers 11th - 12th Standards
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...

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