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Math 214 - Quiz 12 Properties of Subspaces
In this subspace activity, students match a matrix to its property of subspace. This two-page activity contains five problems.
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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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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: 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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Dimensions of Subspaces
In this math worksheet, students practice to find the dimensions of subspaces. They also find the solutions to the systems of equations using the matrices.
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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: 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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Projections of a Vector Onto a Subspace
For this math worksheet, students practice reading the examples of a vector onto a subspace. They also examine the projection matrix.
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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: 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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Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank lesson, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
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Linear Systems: Projections
In this projection worksheet, students determine the projections of a given matrix. This four-page worksheet contains explanations and examples and approximately ten problems to complete.
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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: Projections
In this projection worksheet, students explore the intuition behind projections. They calculate the length using the norm and find the projection of a vector. This two-page worksheet contains approximately five problems.
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Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra instructional activity, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page instructional activity contains examples, explanations, and approximately...
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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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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: Definition of the Nullspace
In this nullspace instructional activity, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page instructional activity contains...
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Extra Problems For Homework 7: Dimension
For this dimension worksheet, students explore manifolds of dimension and find equivalence relations. This one-page worksheet contains three multi-step problems.
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Hints and Extra Problems for Homework 8: Metric Space
In this metric space instructional activity, students determine if a function is continuous and find the metric space. This one-page instructional activity contains three problems.
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Linear Independence, Bases and Coordinate Systems
Students define vocabulary related to vectors and investigate vector problems. In this math lesson, students define basis and explore plotting vectors in correlation to their basis. Plotting polynomials facilitates student understanding.