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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: 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...
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Linear Systems: Vector Spaces
For this vector space worksheet, students explore linearly independent vectors. They identify the row space, null space and subspaces of a given matrix. This four-page worksheet contains approximately eight problems.
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Linear Systems: Column Space and Nullspace of a Matrix
In this column space and nullspace of a matrix worksheet, students are give a three by three matrix. They describe the kind of subspace it is. Students find the nullspace of the matrix.
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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: Lengths and Dot Products
In this dot product worksheet, students explore the multiplication of vectors. This two-page worksheet contains explanations, examples, and approximately ten 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: Applications of Determinants
In this determinant worksheet, students use determinants to find area and volume. This two-page worksheet contains examples, explanations and four problems.
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Linear Systems: Permutations and Transposes
In 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 Determinant
In this determinant activity, students explore the determinant of a matrix. After examining the given examples and explanations, they find the determinants of given matrices. This two-page activity contains nine problems.
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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. ...
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Linear Systems: The Reduced Row Echelon Matrix
In this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page learning exercise 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: 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: 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 activity, students explore a permutation matrix, symmetric matrix, and the properties of the transpose. This three-page activity contains six problems.
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Linear Systems: Methods of Computing Determinants
In this determinant worksheet, 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 worksheet contains explanations,...
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Linear Systems: Eigenvalues and Eigenvectors
For 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: Diagonalizing a Matrix
In this diagonalizing a matrix worksheet, students explore matrix factorization and use diagonal decomposition. This two-page worksheet contains examples, explanations and four 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: Gauss-Jordan Elimination
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: 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.
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this eigenvalue and eigenvector activity, students find the eigenvalue and eigenvector of a given matrix. This two-page activity contains four problems.
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