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MA 371 Homework 1: Vectors
For this vectors worksheet, students solve 7 short answer problems. Students find vectors that are orthogonal. Students solve systems of equations by converting matrices into reduced row echelon form.
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Worksheet 5 - Vectors & Physics
For this vectors worksheet, students determine the amount of work it takes to move objects, they determine if vectors are parallel or orthogonal and identify the displacement direction and the force direction. This one-page worksheet...
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MA 371 - Vector Norm: Dot Product
In this dot product worksheet, students solve 6 short answer problems. Students find unit vectors in the same direction as a given vector. Students express vectors as a linear combination of the standard basis vectors. Students find a...
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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: 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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Matrices and Vectors
In this matrices and vectors worksheet, learners solve 9 various types of problems related to forming matrices and vectors. First, they set up each system of equations listed in matrix form using mathematical notation. Then, students...
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Worksheet 4 - Geometric Mean
In this geometric worksheet, students examine the geometric and algebraic definition of the dot product. They find angles between two curves, determine if two vectors are parallel, and explain conditions on vectors. This one-page...
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Worksheet 24 Spring 1996
For this math worksheet, students find all the vectors in three dimensional space that have the length of 4. Also, the first and third components are the same. Finally, the second component is the sum of the first and third components.
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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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The Haar Wavelet Filter Bank
In this Haar Wavelet learning exercise, students solve and complete 4 different problems related to the Haar Wavelet filter bank. First, they define the properties of Haar basis. Then, students compute the matrices for the first, second...
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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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Worksheet 37
In this math worksheet, students examine the similarities between three-dimensional geometric vectors and Fourier series. Then they write proofs for some of the equations.
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Worksheet 23 Spring 1996
In this math worksheet, students fill in the missing boxes while investigating the concept of vectors. They determine if two vectors are orthogonal or parallel.
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Worksheet 21
In this math worksheet, students draw two vectors u and v based at the same point. The vectors are considered neither parallel nor orthogonal.
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Worksheet 25- Spring 1996
In this math instructional activity, students find the values of the vectors. They also they prove that v and w are both orthogonal and find two nonparallel vectors.
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Worksheet 2
In this math worksheet, students plot the course for a ship traveling from one point to another using two Cartesian coordinates. Then they plot the vector of the course.
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MA 371 Homework 2: Matrices
In this matrices worksheet, students solve 10 short answer problems. Students perform row operations on matrices to find compliments, inverted matrices, orthogonal matrices, etc.
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Omega and Eigenfunction
In this chemistry learning exercise, students calculate the eigenfunction of the operator. They use the operator matrices. There are 4 questions.
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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: 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: 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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More on Least Squares
In this least squares worksheet, students solve 3 different problems that include determining the least squares of equations. First, they use the data given in the table to write out the normal equations a system of 2 equations in 2...
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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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MT-A315 Introduction to Linear Algebra
In this algebra worksheet, students figure out the equation of the general vector, they find the orthogonal basis and apply the formula to solve the problems.