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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: 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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Introduction to Vector Spaces
In this vector spaces activity, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page activity contains 13 problems.
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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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Linear Systems: Vector Spaces of a Matrix
In this vector space matrix activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page activity contains examples and approximately 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: 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: 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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Introduction to Linear Algebra 2.1
In this linear equation instructional activity, students identify the vector space of a given matrices and find the appropriate system of equations for each of four solutions. Then they solve the system and write their conclusion.
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Linear Systems: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
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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: General Solutions
In this linear system worksheet, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.
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Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra worksheet, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page worksheet contains examples, explanations, and approximately four 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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Linear Systems: Linear Equations
For 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: Review of Vectors
In this review of vectors worksheet, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page worksheet contains approximately ten problems.
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Complex Analysis: Linear Transformations
For this linear transformation worksheet, students find a series of linear transformations and sketch them. This four-page worksheet contains approximately six problems.
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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: 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: Column Space and Nullspace of a Matrix
In this matrix worksheet, students find the column space and nullspace of a matrix. They give examples of vectors. This two-page worksheet contains four problems.
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MT-A315 Introduction to Linear Algebra: Worksheet 1.5
In this linear algebra worksheet, students examine a matrix, determine the vectors, list the parameters, and identify the null space. Students explain the parameters in the description of the null space There are four problem solving...
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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: Nullspace Matrix and Rank
In this nullspace matrix learning exercise, 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 learning exercise...