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Linear Systems: Vector Spaces and Subspaces
In this vector space learning exercise, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page learning exercise contains approximately six multi-step...
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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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Least Squares
In this least squares worksheet, students solve 6 different problems that include the least squares of numbers. First, they plot 3 points on the axes shown and draw in their best approximating line. Then, students estimate the slope and...
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Linear Equations and Matrices
Young scholars solve systems of equations. In this precalculus lesson,students solve linear equations using matrices. They use the Gaussian elimination method to identify the missing variables and simplify the linear equations.
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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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Math 214: Quiz 9 - Dimensions of Subspaces
In this subspace activity, students determine the dimension of a nullspace and column space of a given matrix. This two-page activity contains three problems.
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It All Adds Up -- Puzzle Matrix #9
In this addition puzzle worksheet, students find the 7 missing numbers that make all of the rows, columns, and diagonals add up to the given numbers.
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Determinants
In this determinants worksheet, 9th graders solve 10 different problems that include different matrices. They calculate the determinant of each matrix using the data given for each. Then, students define the 2 X 2 matrix and its...
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MT-A314 Introduction to Linear Algebra: Worksheet 4.4
In this linear algebra instructional activity, students prove that a given matrix is orthogonal. In addition, they list the entries for the second column of a matrix and make comparisons. Students complete three problems.
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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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It All Adds Up -- Puzzle #14
In this addition puzzle matrix worksheet, students insert 8 numbers in the puzzle to make the rows, columns, and diagonals add up to the proper numbers.
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It All Adds Up -- Puzzle #15
In this addition matrix puzzle worksheet, students insert 8 numbers into the matrix so the numbers add up diagonally, vertically, and horizontally.
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It All Adds Up -- Puzzle #30
In this addition matrix puzzle worksheet, students insert 8 numbers that make the puzzle add up horizontally, vertically, and diagonally.
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Magic Squares
In this magic squares worksheet, students solve 3 different magic squares shown on the sheet. First, they identify the numbers already used in each square. Then, students determine which number goes in each blank to equal the same sum in...
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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: 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: 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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More on Least Squares
In this least squares instructional activity, 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...
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Introduction to Vector Spaces
In this vector spaces learning exercise, students identify the vector in a given set. They explore addition and scalar multiplication in their vectors. This two-page learning exercise contains 13 problems.
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Magic Square
In this algebra worksheet, 9th graders solve a riddle like puzzle involving matrices and linear equations. They have to find the missing numbers in the square, using the given numbers.
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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: Permutations and Transposes
In this permutations worksheet, students identify a transpose matrix, and create a permutation matrix. This three-page worksheet contains six problems.
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Linear Systems: Vector Spaces
For this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...
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Cramer's Rule
In this algebra worksheet, students solve problems with matrices. They add, subtract and multiply matrices. There are 7 questions.