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Multivariable calculus: Partial Derivatives
In this partial derivative learning exercise, students calculate the derivative of given problems and find the equation of the tangent plane to an equation. This two-page learning exercise contains five problems.
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Multivariable Calculus: Vector Functions
In this vector function worksheet, 12th graders identify a helix and a smooth curve. They find the equation of the tangent line to a helical curve. This two-page worksheet contains examples, explanations and approximately four problems.
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Multivariable Calculus: Linear Systems
In this linear system worksheet, students compute the determinant of a given matrix. They solve systems of equations and compute the inverse of a matrix. This two-page worksheet contains examples, explanations, and three multi-step...
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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: Projections
For 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: Vector Spaces of a Matrix
In this vector space matrix worksheet, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page worksheet contains examples and approximately five problems.
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Linear Systems: Least Squares Approximations
In this least squares approximation instructional activity, 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...
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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: Applications of Eigenvalues and Eigenvectors
In this Eigenvalue worksheet, students examine the applications of matrix exponentiation. This four-page worksheet contains examples, explanations and approximately three problems to complete.
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Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors
In this interpretation of eigenvalues and eigenvectors worksheet, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
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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: Symmetric Matrices
In this symmetric matrices worksheet, students find the eigenvalues of a matrix and discover that symmetric matrices are diagonalizable. This two-page worksheet contains examples, explanations and two problems.
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Linear Systems: Differential Equations
In this differential equations worksheet, students solve collections of simultaneous differential equations. This six-page worksheet contains examples, explanations, and approximately six problems.
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Linear Systems: Vector Spaces and Subspaces
In this vector spaces and subspaces learning exercise, 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...
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Linear Systems: Nullspace
For 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: Rectangular Matrices
In this rectangular matrices worksheet, students complete solutions to given matrices. They identify the pivot columns and examine the nullspace of a matrix. This four-page worksheet contains examples, explanations and approximately...
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Linear Systems: Nullspace Matrix
In this linear systems learning exercise, students explore the dimensions of a matrix. They identify the independent rows and columns. This two-page learning exercise contains explanations, examples and four problems to solve.
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Linear Systems: Reduced Row Echelon Matrix and Rank
Students find the nullspace of the three matrices by finding the reduced row echelon matrix for each in this activity. They convert three matrices to reduced row echelons and show they have only one pivot. Students find the rank of three...
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Linear Systems: Vector Spaces
In 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: 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: Lengths and Dot Products
In this dot product activity, students explore the multiplication of vectors. This two-page activity contains explanations, examples, and approximately ten problems.
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Linear Systems: Matrix Operations
This matrix operations worksheet covers topics such as matrix addition, multiplication and properties such as associative, commutative and distributive. Students give examples and counter examples of matrix addition and multiplication. ...
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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: Using Matrix Operations
In this matrix operations worksheet, students convert a system of linear equations into a matrix. This four-page worksheet contains explanations, examples and four problems.
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