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Linear Systems: Definition of the Nullspace
In this nullspace worksheet, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page worksheet contains approximately 8 problems.
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Linear Systems: Reduced Row Echelon Matrix
In this echelon matrix worksheet, learners find the nullspace of matrices by finding the reduced row echelon. This two-page worksheet contains explanations, examples and six problems to complete.
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Linear Systems: Orthogonality of Subspaces
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: Independence, Basis and Dimension
In this basis and dimension learning exercise, students explore vector spaces associated with rectangular matrices. The two-page learning exercise contains approximately 20 short answer questions.
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Linear Systems: Fundamental Theorem
In this fundamental theorem instructional activity, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page...
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Systems-Angle Problems
In this geometry worksheet, 10th graders use systems of linear equations to solve word problems which involve supplementary and complementary angles. The one page worksheet contains ten problems. Answers are not provided.
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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.
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Linear Systems: Symmetric Matrices
In this symmetric matrices worksheet, students find the eigenvalues of a matrix and discover that symmetric matrices are diagonalizable. This two-page worksheet contains examples, explanations and two problems.
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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: Permutations and Transposes
For this permutation worksheet, students multiply matrices, explore symmetric matrices, permutation matrices, and properties of the transpose. This three-page worksheet contains explanations, examples and four problems.
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Linear Systems: The Reduced Row Echelon Matrix
For this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page worksheet contains explanations, examples and six problems.
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Linear Systems: The Nullspace Matrix and Rank
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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Linear Systems: Matrix Multiplication
In this matrix multiplication learning exercise, students multiply matrices and identify the rotation matrix of a given angle. This two-page learning exercise contains examples, explanations and two problems to solve.
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Linear Systems; Permutations and Transposes
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: Eigenvalues and Eigenvectors
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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Linear Systems and Reviewing for Exam 2
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: The Inverse Matrix
In this inverse matrix instructional activity, students find the product of matrices. They generate an inverse matrix using the Gauss-Jordan elimination method. This two-page instructional activity contains explanations, examples and...
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this Eigenvalue activity, students examine the applications of matrix exponentiation. This four-page activity contains examples, explanations and approximately three problems to complete.
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Linear Systems: Properties of the Four Matrix Subspaces
In this four matrix subspaces worksheet, students identify statements which are always true for given matrices. Students are given five matrices and a list of ten statements.
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Linear Systems: The Determinant
In this determinant worksheet, students explore the determinant of a matrix. After examining the given examples and explanations, they find the determinants of given matrices. This two-page worksheet contains nine problems.
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this eigenvalue and eigenvector worksheet, students find the eigenvalue and eigenvector of a given matrix. This two-page worksheet contains four problems.
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Linear Systems: Column Space and Nullspace of a Matrix
In this matrix instructional activity, students find the column space and nullspace of a matrix. They give examples of vectors. This two-page instructional activity contains four problems.
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Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors
In this interpretation of eigenvalues and eigenvectors worksheet, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
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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...