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Linear Systems: Reduced Row Echelon Matrix and Rank
Students find the nullspace of the three matrices by finding the reduced row echelon matrix for each in this activity. They convert three matrices to reduced row echelons and show they have only one pivot. Students find the rank of three...
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Row-Echelon Matrices
In this algebra activity, students rewrite linear equations using matrices and solve using row-echelon form. There are 30 problems ranging from one equation to system of equations.
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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: The Reduced Row Echelon Matrix
In this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page worksheet contains explanations, examples and six problems.
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MA 371 - Reduced Row Echelon Form
In this reduced row echelon form worksheet, students solve 2 short answer problems. Students find the reduced row echelon form of a matrix using row operations.
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Augmented Matrices
Pupils write systems of equations in an augmented matrix and enter it into their calculator. They use the reduced row echelon function on the calculator to solve the system of equations.
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Exercises for Section 5.3: Matrices
In this matrices worksheet, students solve 26 systems of equations using matrices. Students solve each system using matrices. Students determine the rank and solutions of each matrix using row echelon form of each system.
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Linear Systems
In this linear systems 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 the column...
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Linear Systems and Echelon Forms
Eleventh graders define various types of linear systems and three types of solutions. In this linear system and echelon forms instructional activity, 11th graders solve a linear system using elementary row operations. Students also...
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Solving Systems with Row Operations 2
Have your class solve equations using matrices by teaching them how to factor systems of equation to identify the point of intersection. They create their matrices on the Ti and perform row operations to simplify.
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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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Linear Systems: Nullspace
In this nullspace worksheet, students explore vectors and nullspaces found in a matrix. They convert augmented matrix to echelon form. This six-page worksheet contains approximately ten problems.
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Solving Systems with Row Operations 1
Students solve systems of equations. In this algebra lesson, students use matrices to solve linear equations. They use reduced row echelon-form and scalar multiplier to simplify the matrices completely.
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MA 371 - Linear Equations 1
In this linear equations worksheet, students solve 8 short answer problems. Students write augmented matrices given a system of equations in two and three variables. Students express their answers using an augmented matrix in reduced row...
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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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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...
PBL Pathways
Gas Prices
How can math help your vehicle run better? Complete an interesting project-based learning task with your classes to determine the cheapest approach to mixing the ideal octane level of gasoline. Scholars create and solve a system of...
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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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Solution Sets and Linear Independence of Vectors
Eleventh graders study homogeneous linear systems. In this linear system of equations lesson, 11th graders write linear system solutions in parametric vector form. Students also identify the connection between linear independence and...
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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.