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MA 371 - Matrices: Solving Systems and Determinants
In this solving systems and determinants worksheet, learners solve 4 multi-part short answer problems. Students solving systems of equations using matrices. Learners find a basis for row spaces and column spaces. Students find the...
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Compare-Contrast Matrix Maker
Check out this amazing, customizable graphic organizer. You can create as many grids as you'd like with two to five columns and three to seven columns. The title is editable as are the labels for the columns and the rows. The process is...
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Linear Systems: The Column Space
For this column space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples of and explanations. One problem is provided for students to complete.
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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: Column Space and Nullspace of a Matrix
In this matrix learning exercise, students find the column space and nullspace of a matrix. They give examples of vectors. This two-page learning exercise contains four problems.
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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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Linear Systems: Vector Spaces and Subspaces
In this vector space worksheet, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page worksheet contains approximately six multi-step 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: 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: 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: 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: Orthogonality of Vector Spaces of a Matrix
In this vector spaces of a matrix worksheet, students decompose any vector into two orthogonal pieces. They identify the nullspace, row space, and find a reduced echelon. This two-page worksheet contains examples and two problems.
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Linear Systems
In 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: Fundamental Theorem
In this fundamental theorem worksheet, 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 worksheet...
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Linear Systems: Reduced Row Echelon Matrix
For this echelon matrix worksheet, students 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: 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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Introduction to Vector Spaces
In this vector spaces instructional activity, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page instructional activity contains 13 problems.
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Linear Systems: Vector Spaces
In this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...
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Math 214: Quiz 9 - Dimensions of Subspaces
In this subspace learning exercise, students determine the dimension of a nullspace and column space of a given matrix. This two-page learning exercise contains three problems.
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Linear Systems: Orthogonal Matrices
In this orthogonal matrices worksheet, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page worksheet contains approximately six...
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Introduction to Networks
Watch as matrices break networks down into rows and columns! Individuals learn how a network can be represented as a matrix. They also identify the notation of matrices.
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Linear Systems: Linear Equations
In this linear systems instructional activity, students use a matrix to represent linear systems. This four page instructional activity provides examples, explanations and approximately eight problems to complete.
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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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More on Least Squares
In this least squares activity, students solve 3 different problems that include determining the least squares of equations. First, they use the data given in the table to write out the normal equations a system of 2 equations in 2...