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Linear Systems: Matrix Operations
This matrix operations worksheet covers topics such as matrix addition, multiplication and properties such as associative, commutative and distributive. Students give examples and counter examples of matrix addition and multiplication. ...
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Linear Systems: Fundamental Theorem
In this fundamental theorem learning exercise, students show matrix multiplication, identify the vector in the nullspace and interpret equations. This two-page learning exercise contains examples, explanations and three problems.
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Solving Equations Involving Linear Transformations of the Coordinate Plane
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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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.
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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...
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Matrices
In this Algebra II worksheet, 11th graders determine if matrices are inverses, multiply matrices, and solve matrix equations. The three page worksheet contains explanation of topic, worked examples, and five practice problems. Answers...
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Basic Matrix Algebra
Students perform basic matrices operations. In this algebra lesson, students add, subtract, multiply and divide matrices. They solve system of equations using matrices.
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Complex Numbers and Transformations
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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Exploiting the Connection to Cartesian Coordinates
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
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Linear Systems
In this linear systems worksheet, learners solve and complete 10 different problems that include writing each as a linear equation. First, they write the systems of linear equations represented by each matrix equation. Then, students...
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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...
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Matrix operations and Matrix Inverses
Eleventh graders study how to combine like vector's that are matrices. In this matrix operations worksheet, 11th graders combine matrices linearly and define the matrix-matrix product and its properties. Students also study matrix...
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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.
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Linear Equations and Matrices
Young scholars solve systems of equations. In this precalculus lesson,students solve linear equations using matrices. They use the Gaussian elimination method to identify the missing variables and simplify the linear equations.
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Linear Systems: LU Decomposition
In this LU decomposition worksheet, students multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page worksheet contains approximately six problems.
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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.
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Coded Messages
High schoolers solve matrices by multiplication. In this algebra lesson, students create coded messages and relate it to solving matrices. They multiply and find the inverse of matrices.
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Solving Linear Systems Using Matrices
Start with the definition of a determinant and how to evaluate a 2x2 determinant. Apply this skill to solve systems of two equations with two unknowns by using Cramer's rule. These four basic problems would be good for a quick review or...
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The Binomial Theorem
Students simplify 3 series multiplication problems, one fraction , and six matrix problems. They expand 12 binomials, Students find the specified term of four binomials.
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Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra worksheet, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page worksheet contains examples, explanations, and approximately four problems to complete.
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Representing Reflections with Transformations
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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Vectors and Translation Maps
Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...
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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...
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Areas of Polygons
Young mathematicians calculate the area of polygons in this algebra lesson. They find the determinant as they calculate the areas for triangles and quadrilaterals. They also use scalar multiplication to find the determinant.