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Linear Systems: Vector Spaces and Subspaces
In 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: 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 worksheet, learners 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: 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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Eliminate What?
Learners are introduced to the elimination method in Algebra. As a class, they solve two linear equations with two unknowns using this new method. They discuss the positive and negative aspects of using this method to solve problems. ...
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Cramer's Rule ID: 8793
Mathematicians are introduced to Cramer’s Rule and use it to solve three systems that have one solution, no solutions, and an infinite number of solutions. High schoolers use TI-Nspire to graph the systems to verify their answers...
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Worksheet 1, Basic Calculus Pre-Course Review
In this calculus worksheet, learners review topics they need to already understand in order to be successful in a basic calculus course. Topics include functions, linear equations, coordinate graphing, piece-wise formulation, exponents,...
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Grab Bags
Eighth graders graph two inequalities with a single variable. They include drawing the intersection or union of inequalities on a number line. Students solve the linear equations using properties of equality and inequality. The lesson...
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A Point of Intersection
Pupils factor and solve systems of equation. In this algebra lesson, students identify the point of intersection using substitution, elimination and graphing. They write an equation given a system and a graph.
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Whose Line is it Anyway?
Students solve systems of equations. In this algebra lesson plan, students identify the domain and range of each function. They use the slope and y-intercept to graph each line.
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Minima/Maxima
In this minima/maxima worksheet, students solve systems of equations, identify the first derivative of a quadratic equation, and find the critical point in an equation. Using Excel worksheets, students graph four equations. There are...
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Worksheet 13
In this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.
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Count the Differences
Pupils find the difference between consecutive y-values on the calculator and write an equation that fits the data. They continue finding the differences in consecutive y-values using lists on their calculator. Learners...
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Academic Algebra II 1st Semester Exam
In the semester exam, students solve problems dealing the the discriminant of quadratic equations, systems of equations, linear equations and inequalities. Students also simplify radicals, complete squares, and find the inverse...
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Linear Systems: Vector Spaces of a Matrix
In this vector space matrix instructional activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page instructional activity contains examples and...
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Linear Systems: Projections
In this projection worksheet, learners 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 instructional activity, 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...
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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: Vector Spaces and Subspaces
In this vector spaces and subspaces worksheet, 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 vector...
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Linear Systems: Column Space and Nullspace of a Matrix
In this column space and nullspace of a matrix worksheet, students are give a three by three matrix. They describe the kind of subspace it is. Students find the nullspace of the matrix.
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Linear Systems: Properties of the Four Matrix Subspaces
In this four matrix subspaces worksheet, students identify statements which are always true for given matrices. Students are given five matrices and a list of ten statements.
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Linear Systems: Lengths and Dot Products
In this dot product instructional activity, students explore the multiplication of vectors. This two-page instructional activity contains explanations, examples, and approximately ten problems.
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