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Minima/Maxima
In this minima/maxima worksheet, students solve systems of equations, identify the first derivative of a quadratic equation, and find the critical point in an equation. Using Excel worksheets, students graph four equations. There are...
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Work in Linear Mechanical Systems
Young scholars are able to identify the units associated with linear work. They are able to calculate the work done on an object. Students discover how the force exerted on an object and the distance the object moves determines the...
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Worksheet 13
In this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.
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Academic Algebra II 1st Semester Exam
In the semester exam, learners solve problems dealing the the discriminant of quadratic equations, systems of equations, linear equations and inequalities. Students also simplify radicals, complete squares, and find the inverse...
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Linear Systems: Vector Spaces of a Matrix
In this vector space matrix learning exercise, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page learning exercise contains examples and approximately five...
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Linear Systems: Projections
In this projection worksheet, students determine the projections if a given matrix. They take a vector and project it onto a line and subspace. This four-page worksheet contains examples and approximately seven problems.
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this Eigenvalue learning exercise, students examine the applications of matrix exponentiation. This four-page learning exercise contains examples, explanations and approximately three problems to complete.
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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: 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
For 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: 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 learning exercise, students explore the multiplication of vectors. This two-page learning exercise 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 learning exercise, students use determinants to find area and volume. This two-page learning exercise 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 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: 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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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 learning exercise, students identify the rank and nullspace in a matrix. They compare the nullspace and column space of given matrices. This two-page learning exercise 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 worksheet, students multiply matrices and identify the rotation matrix of a given angle. This two-page worksheet 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.