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Cramer's Rule
In this Cramer's Rule worksheet, students first evaluate five determinants or square matrix. Then they solve the last five problems by applying Cramer's Rule. Students identify and define Cramer's Rule as a theorem used with linear...
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Linear Systems Review Problems
In this linear systems activity, students identify the requirements for two linear systems to have at least one solution. They find a matrix with no zero entries that has the given fully reduced form. Students use row reduction to...
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Multivariable Calculus: Linear Systems
In this linear systems worksheet, students perform matrix multiplication. This two-page worksheet contains examples, explanations, definitions, and four 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: 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: 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 Operations
In this matrix operations worksheet, students perform matrix addition and multiplication. This two-page worksheet contains six problems. Definitions, examples and explanations are also provided.
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Linear Systems: Using Matrix Operations
In this linear systems worksheet, learners use matrix multiplication as an elimination technique to solve linear systems. They compare products and explore trends. This four-page worksheet contains explanations, examples and five...
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Linear Systems: LU Decomposition
In this LU decomposition activity, students multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page activity contains approximately six problems.
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Linear Systems: Vector Spaces and Subspaces
In this vector space learning exercise, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page learning exercise contains approximately six multi-step...
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Linear Systems: Reduced Row Echelon Matrix
For 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: Nullspace Matrix and Rank
In this nullspace matrix worksheet, students observe the rank and number of independent rows and columns a matrix has. They compute the product of matrices and describe the column space of each. This two-page worksheet contains...
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Linear Systems
For this linear systems worksheet, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the column...
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Linear Systems: Linear Equations
In this linear systems worksheet, students use a matrix to represent linear systems. This four page worksheet provides examples, explanations and approximately eight problems to complete.
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Linear Systems: Nullspace
In 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: 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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Math 214 Quiz 5 - Eigenvalues
In this eigenvalue learning exercise, students answer true and false questions about eigenvalues. They must support their answer with an explanation. This two-page learning exercise contains three questions.
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Math 214: Quiz 9 - Dimensions of Subspaces
In this subspace activity, students determine the dimension of a nullspace and column space of a given matrix. This two-page activity contains three problems.
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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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Other Methods of Computing Determinants
In 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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The Column Space of a Matrix
In this math worksheet, students 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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The Nullspace of a Matrix
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.