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Linear Independence, Bases and Coordinate Systems
Students define vocabulary related to vectors and investigate vector problems. In this math lesson, students define basis and explore plotting vectors in correlation to their basis. Plotting polynomials facilitates student understanding.
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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
In this linear systems instructional activity, 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...
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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...
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MA 371 - Matrices: Solving Systems and Determinants
In this solving systems and determinants worksheet, students solve 4 multi-part short answer problems. Students solving systems of equations using matrices. Students find a basis for row spaces and column spaces. Students find the...
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MT-A315 Introduction to Linear Algebra
In this algebra instructional activity, students practice using number sets and principles of algebra to solve each complex problem using number sense.
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Complex Analysis: Linear Transformations, Inversion Mappings
In this transformation learning exercise, students identify a series of transformations and sketch them. They use inversion mapping to establish a one-to-one correspondence between nonzero points. This four-page learning exercise...
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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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Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank activity, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
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MT-A315 Introduction to Linear Algebra
For 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.
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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: Reduced Row Echelon Matrix
In this echelon matrix learning exercise, students find the nullspace of matrices by finding the reduced row echelon. This two-page learning exercise contains explanations, examples and six problems to complete.
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Automobile-Accident Reconstruction
Students investigate an accident and relate it to math. In this trigonometry instructional activity, students measure the accident scene, the friction produced, and the speed from the skid marks. They create a poster of their findings.
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Sciences Working Together
High schoolers research articles about science technology and society. In this science and technology instructional activity, students answer questions about an article they chose. They share what they learned with their peers.