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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: Differential Equations
In this differential equations worksheet, students solve collections of simultaneous differential equations. This six-page worksheet contains examples, explanations, and approximately six problems.
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Linear Systems: Vector Spaces and Subspaces
In this vector spaces and subspaces learning exercise, 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...
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Linear Systems: Nullspace
For this nullspace worksheet, students explore vectors and nullspaces found in a matrix. They convert augmented matrix to echelon form. This six-page worksheet contains approximately ten problems.
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Linear Systems: Rectangular Matrices
In this rectangular matrices worksheet, students complete solutions to given matrices. They identify the pivot columns and examine the nullspace of a matrix. This four-page worksheet contains examples, explanations and approximately...
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Linear Systems: Nullspace Matrix
In this linear systems learning exercise, students explore the dimensions of a matrix. They identify the independent rows and columns. This two-page learning exercise contains explanations, examples and four problems to solve.
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Linear Systems: Reduced Row Echelon Matrix and Rank
Students find the nullspace of the three matrices by finding the reduced row echelon matrix for each in this activity. They convert three matrices to reduced row echelons and show they have only one pivot. Students find the rank of three...
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Linear Systems: Vector Spaces
In 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: Graphical Interpretation of Vectors and Linear Systems
In this interpretation of vectors and linear systems worksheet, students describe the geometric appearance of two vectors. They add the two vectors and sketch the sum as well as the vectors to determine the commutativity of vector...
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Linear Systems: Lengths and Dot Products
In this dot product activity, students explore the multiplication of vectors. This two-page activity 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: Linear Equations, Vectors and Matrices
In this matrices worksheet, students write matrix notation to represent linear systems. This four-page worksheet contains approximately 15 problems.
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Linear Systems: Using Matrix Operations
In this matrix operations worksheet, students convert a system of linear equations into a matrix. This four-page worksheet contains explanations, examples and four problems.
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Linear Systems: Identifying Pivots and Multipliers
In this pivot worksheet, students explore the elimination process, and write a matrix in upper triangular form. They identify equivalent systems. This four-page worksheet contains examples, explanations, and approximately ten problems.
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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 instructional 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 instructional activity contains...
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Introductions to Eigenvalues and Eigenvectors
In this math worksheet, students solve the problems that are related to the finding of the eigenvalues and eigenvectors. They must show all their work for the answers.
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Linear Systems: The Matrix Inverse
In this matrix inverse worksheet, 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. This four-page...
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Other Methods of Computing Determinants
For this math worksheet, students find the answers to the problems related to computing determinants. They read the examples and progress from one step to the next.
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Diagonalizing a Matrix
In this math worksheet, students find the answers to the problems that focus upon the concept of diagonalizing a matrix. They also find the probability matrix.
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Linear Systems: Differential Equations
In this differential equations worksheet, students determine the stability of matrices and evaluate a matrix with an exponent. This two-page worksheet contains examples, explanations, and two problems to solve.
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Applying Linear Algebra to Differential Equations
In this math activity, students using linear algebra to find the solutions to the differential equations. The equations are listed in systems.
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The Column Space of a Matrix
In this math worksheet, learners find the answers to the problems that are related to using a matrix. They group the numerical values with the matrix.
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