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Linear Algebra
In this linear algebra worksheet, students solve 3 different sets of problems that include rank, dimension, nullspace and range of linear algebra. They determine the relation between the rank of a matrix and the dimension of its range....
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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: 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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Linear Systems: Orthogonality of Vector Spaces of a Matrix
In this vector spaces of a matrix activity, students decompose any vector into two orthogonal pieces. They identify the nullspace, row space, and find a reduced echelon. This two-page activity contains examples and two problems.
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Linear Systems: Vector Spaces
For 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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Linear Systems: Nullspace Matrix and Rank
For 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: 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
For this linear systems worksheet, students explore the dimensions of a matrix. They identify the independent rows and columns. This two-page worksheet contains explanations, examples and four problems to solve.
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Linear Systems: Vector Spaces
In this vector space learning exercise, students explore linearly independent vectors. They identify the row space, null space and subspaces of a given matrix. This four-page learning exercise contains approximately eight problems.
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Linear Systems: The Reduced Row Echelon Matrix
For this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page worksheet contains explanations, examples and six problems.
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The Nullspace of a Matrix
In this math activity, students read the definition for the nullspace of a matrix. The definition is used to find the solutions to new problems.
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Linear Systems: Fundamental Theorem
In this fundamental theorem worksheet, students show matrix multiplication, identify the vector in the nullspace and interpret equations. This two-page worksheet contains examples, explanations and three problems.
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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.