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Linear Systems: The Reduced Row Echelon Matrix

For Students Higher Ed
In this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page activity contains explanations, examples and six problems.
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The Nullspace of a Matrix

For Students 11th - Higher Ed
In this math instructional activity, students read the definition for the nullspace of a matrix. The definition is used to find the solutions to new problems.
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Linear Systems: The Nullspace Matrix and Rank

For Students Higher Ed
In this nullspace worksheet, students identify the rank and nullspace in a matrix. They compare the nullspace and column space of given matrices. This two-page worksheet contains examples, explanations and five problems.
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Projections of a Vector Onto a Subspace

For Students 11th - Higher Ed
In this math activity, learners practice reading the examples of a vector onto a subspace. They also examine the projection matrix.
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General Solution to Ax=b

For Students 11th - Higher Ed
In this math instructional activity, students practice finding the vector spaces associated with the rectangular matrices. Then they find the complete solutions to the given equation using a matrix.
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Linear Systems: Fundamental Theorem

For Students Higher Ed
In this fundamental theorem worksheet, students show matrix multiplication, identify the vector in the nullspace and interpret equations. This two-page worksheet contains examples, explanations and three problems.
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Linear Systems Class Overview

For Students 11th - Higher Ed
In this math instructional activity, students find the solutions to the problems using the linear systems of equations. The sheet is a list of review topics.
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Linear Systems: Orthogonality of Subspaces

For Students Higher Ed
In this subspace worksheet, students decompose a vector into two orthogonal pieces, one for the nullspace and another for the row space of a matrix. This two-page worksheet contains explanations, examples, and three problems.
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Linear Systems; Permutations and Transposes

For Students Higher Ed
In this permutations worksheet, students explore a permutation matrix, symmetric matrix, and the properties of the transpose. This three-page worksheet contains six problems.
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Linear Systems: Methods of Computing Determinants

For Students Higher Ed
In this determinant activity, students explore the properties of the determinant. They compute determinants by using the co-factor method, the "big formula" and the product of pivots. This two-page activity contains explanations,...
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Linear Systems: Eigenvalues and Eigenvectors

For Students Higher Ed
In this eigenvalues worksheet, students find the eigenvalues and eigenvectors of a given matrix. This two-page worksheet contains examples, explanations and two practice problems.
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Geometric Interpretations of Eigenvalues and Eigenvectors

For Students 11th - Higher Ed
In this math learning exercise, students practice finding the Eigenvalues and Eigenvectors. They find the special factors of the given matrices.
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Linear Systems and Reviewing for Exam 2

For Students 11th - Higher Ed
In this math worksheet, students practice reviewing the different method to find the inverse for a matrix. They compute the determinant of a matrix.
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Linear Systems: Graphical Interpretation of Vectors

For Students Higher Ed
In this graphical interpretation of vectors instructional activity, students explore the geometrical appearance of given problems, determine if vector subtraction is commutative and graph a system of equations. This three-page...
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Linear Systems: Elimination

For Students Higher Ed
In this elimination worksheet, students use the elimination process to transform a system into an equivalent form. This three-page worksheet contains three practice problems as well as examples and explanations.
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Lengths and Dot Sequences

For Students 11th - Higher Ed
In this math learning exercise, students examine the process of multiplying vectors to find their products. They practice finding the geometric and algebraic views for the solutions.
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Linear Systems: Linear Equations, Vectors and Matrices

For Students Higher Ed
In this vector and matrix worksheet, students explore matrix notation to represent linear systems. They use geometric interpretations of linear systems. This three-page worksheet contains three practice problems, explanations and...
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Linear Systems/ LU Decomposition

For Students 11th - Higher Ed
In this math instructional activity, learners find the values by factoring a matrix A into the product of a lower triangular matrix L. They also make it into an upper matrix U.
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Linear Systems: Gauss-Jordan Elimination

For Students Higher Ed
In this Gauss-Jordan worksheet, students use the Gauss-Jordan method to find an identify matrix. This two-page worksheet provides examples, explanations and two practice problems.
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Linear Systems Review for Exam 1

For Students 11th - Higher Ed
In this math instructional activity, students practice reviewing for the exam that focuses upon the concept of linear systems. They draw a concept map for the review topics listed.
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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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Linear Systems: Matrix Operations

For Students Higher Ed
In this matrix operations worksheet, students find the dot product of matrices. They use the elimination method to solve linear equations. This two-page worksheet contains explanations, examples and three problems.
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Elimination: Using Matrix Operations

For Students 11th - Higher Ed
In this math worksheet, students practice using a matrix with the method of elimination to find the solutions. They practice using matrix multiplication.
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Introduction to Taylor Series

For Students Higher Ed
In this Taylor series worksheet, students determine the difference between a Taylor series and a Taylor polynomial. They solve function problems. This two-page worksheet contains seven problems.

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