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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: Review of Vectors
In this review of vectors activity, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page activity contains approximately ten problems.
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Linear Systems: Graphical Interpretation of Vectors
In this graphical interpretation of vectors activity, students execute operations of addition and multiplication by a scalar. They sketch results and determine the commutativity of vector addition. This three-page activity contains...
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Linear Systems: Least Squares Approximations
In this least squares approximation worksheet, students determine the number of solutions a given linear system has. They find the least square error and the equation of a line of best fit for a set of three points. Students find the...
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Linear Systems: Graphical Interpretation of Vectors and Linear Systems
In this interpretation of vectors and linear systems worksheet, students describe the geometric appearance of two vectors. They add the two vectors and sketch the sum as well as the vectors to determine the commutativity of vector...
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Linear Systems: Matrix Operations
In this matrix operations learning exercise, students perform matrix addition and multiplication. This two-page learning exercise contains six problems. Definitions, examples and explanations are also provided.
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Linear Systems: Using Matrix Operations
In this linear systems worksheet, students 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 worksheet, learners multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page worksheet contains approximately six problems.
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Linear Systems: Matrix Inverse
In this linear systems activity students multiply matrices and find the coefficient matrix in the upper-triangular form. This four-page activity contains approximately four problems, with examples and explanations.
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Linear Systems: The Determinant
In this determinant activity, students find the determinants of matrices. They identify patterns and their relationship to the canonical matrix. This two-page activity contains approximately nine problems, as well as examples and...
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Linear Systems: Permutations and Transposes
In this permutations worksheet, students identify a transpose matrix, and create a permutation matrix. This three-page worksheet contains six problems.
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Linear Systems: Eigenvalues and Eigenvectors
In this "Eigenvalues and Eigenvectors" instructional activity, students find the eigenvalue of a matrix and explore the properties of eigenvalues with a matrix. This two page instructional activity contains two multi-step problems.
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Linear Systems: Other Methods of Computing Determinants
In this computing determinants worksheet, students explore methods of computing determinants. They complete determinant problems by using the co-factor method, the "big formula" and the use of product of the pivots. This two-page...
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Linear Systems: Applications of Determinants
In this determinant worksheet, students explore determinants, area and volume. This two-page worksheet contains explanations and examples. It provides two problems for students to solve.
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Linear Systems: Geometric Interpretation of Eigenvalues
In this geometric interpretation worksheet, students prove the exponentiation of a matrix and the Eigenvalues of an inverse. This two-page worksheet contains explanations, examples, theorems and two problems for students to solve.
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Linear Systems: Applications of Eiginvalues
In this Eigenvalue and Eigenvector learning exercise, students examine the applications of matrix exponentiation. This four-page learning exercise provides explanations and examples, as well as three problems to complete.
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Linear Systems: Vector Spaces and Subspaces
For 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: Reduced Row Echelon Matrix
In 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: 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 multiplication of vectors worksheet, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm...
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Linear Systems: Identifying Pivots and Multipliers
In this identifying pivots worksheet, students use algebra to find equivalent systems of equations. This four-page worksheet contains examples, explanations and approximately ten problems.
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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: 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: Identifying Pivots and Multipliers
For this pivot worksheet, students explore the elimination process, and write a matrix in upper triangular form. They identify equivalent systems. This four-page worksheet contains examples, explanations, and approximately ten problems.