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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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Choosing a College
How can mathematics help scholars choose a college? High schoolers learn how they can use decision matrices to rank colleges based on selected criteria. They also see how to weigh criteria using multiplication of the decision matrix by a...
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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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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
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: Linear Equations
In this linear systems worksheet, students use a matrix to represent linear systems. This four page worksheet provides examples, explanations and approximately eight 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
For this linear systems worksheet, 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 the column...
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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: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
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Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank lesson, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
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Linear Systems: Nullspace Matrix and Rank
In this nullspace matrix worksheet, 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 worksheet contains...
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Matrix operations and Matrix Inverses
Eleventh graders study how to combine like vector's that are matrices. In this matrix operations worksheet, 11th graders combine matrices linearly and define the matrix-matrix product and its properties. Students also study matrix...
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MT-A315 Introduction to Linear Algebra: Worksheet 1.5
In this linear algebra instructional activity, 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...
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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.
EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
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Linear Systems: Matrix Operations
In this matrix operations worksheet, students perform matrix addition and multiplication. This two-page worksheet contains six problems. Definitions, examples and explanations are also provided.
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Matrices and Transformations
For this matrix worksheet, learners explore and solve problems with matrices by addition, subtraction, multiplication and using linear equations. There are 28 problems with some answers.
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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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Linear Systems: Definition of the Nullspace
In this nullspace instructional activity, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page instructional activity contains...
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Linear Systems: General Solutions
In this linear system worksheet, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.
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Linear Systems: Reduced Row Echelon Matrix
For 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: Applications of Eiginvalues
In this Eigenvalue and Eigenvector worksheet, learners examine the applications of matrix exponentiation. This four-page worksheet provides explanations and examples, as well as three problems to complete.
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Four Matrix, Eigenvalue, and Eigenvector Problems
In this matrix worksheet, students solve a system of differential equations, find eigenvalues and eigenvector in two problems, and solve a word problem using a system.