Instructional Video
Sophia Learning

Sophia: Using Elementary Row Operations to Solve for Systems of Equations

For Students 9th - 10th Standards
This video lesson demonstrates how to solve a system of linear equations by using matrix row operations. Students can check their understanding with an assessment.
Instructional Video
Sophia Learning

Sophia: Using Elementary Row Operations to Solve Systems of Equations: Lesson 1

For Students 9th - 10th
This lesson presents how to use elementary row operations to solve for a system of linear equations. It is 1 of 4 in the series titled "Using Elementary Row Operations to Solve for Systems of Equations."
Activity
Stefan Warner and Steven R. Costenoble

Finite Mathematics & Applied Calculus: The Matrix of a System and Row Operations

For Students 9th - 10th Standards
The tutorial examines the matrix of a system and row operations. Students learn about the concepts through class notes, examples, and practice problems. Topics include a system of linear equations and augmented matrices. Review exercises...
Instructional Video
Khan Academy

Khan Academy: More Determinant Depth: Determinant After Row Operations

For Students 9th - 10th
A video showing what happens to the determinant when we perform a row operation.
Instructional Video
Sophia Learning

Sophia: Row Operations: Lesson 2

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 2 of 9 in the series titled "Row Operations."
Instructional Video
Sophia Learning

Sophia: Row Operations: Lesson 4

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 4 of 9 in the series titled "Row Operations."
Instructional Video
Sophia Learning

Sophia: Row Operations: Lesson 5

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 5 of 9 in the series titled "Row Operations."
Instructional Video
Sophia Learning

Sophia: Row Operations: Lesson 8

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 8 of 9 in the series titled "Row Operations."
Instructional Video
Sophia Learning

Sophia: Row Operations: Lesson 9

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 9 of 9 in the series titled "Row Operations."
PPT
Sophia Learning

Sophia: Row Operations: Lesson 1

For Students 9th - 10th
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 1 of 9 in the series titled "Row Operations."
PPT
Sophia Learning

Sophia: Using Elementary Row Operations to Solve Systems of Equations: Lesson 4

For Students 9th - 10th Standards
This lesson presents how to use elementary row operations to solve for a system of linear equations. It is 4 of 4 in the series titled "Using Elementary Row Operations to Solve for Systems of Equations."
PPT
Sophia Learning

Sophia: Row Operations: Lesson 3

For Students 9th - 10th Standards
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 3 of 9 in the series titled "Row Operations."
Lesson Plan
Texas Instruments

Texas Instruments: Matrices and Vectors

For Teachers 9th - 10th Standards
In this activity, students learn to create and edit a matrix using the matrix editor. They use various features in the calculator to perform elementary row operations and convert a matrix to its reduced row echelon form. Finally they...
Activity
Washington State University

Washington State University: Tool for Elementary Row Operations

For Students 9th - 10th
This site from Washington State University is useful to students as it will break down and solve the matrix for them.
Activity
Purple Math

Purplemath: Matrix Row Operations

For Students 9th - 10th
Purplemath explains each of the elementary row operations and goes through explaining how each step is carried out and the common notation for each operation. The lesson ends with an example of how to solve an augmented matrix.
Handout
University College London

University College London: Elementary Row Operations

For Students 9th - 10th
Gives the basics on when to use matrices effectively. Example is included to make things clearer.
Handout
Math Notes and Math Tests

Pre Calculus Notes: Matrices and Systems of Equations [Pdf]

For Students 9th - 10th Standards
Students learn about matrices and systems of equations. Topics explored are elementary row operations, Gaussian elimination, row-echelon form, and systems with infinitely many solutions. Class notes and examples are included.
PPT
Sophia Learning

Sophia: Using Elementary Row Operations to Solve for Systems of Equations

For Students 9th - 10th Standards
This lesson presents how to use elementary row operations to solve for a system of linear equations.
Instructional Video
Khan Academy

Khan Academy: Solving a System of 3 Equations and 4 Variables Using Matrix

For Students 10th - 12th Standards
Sal solves a linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form.
Activity
Stefan Warner and Steven R. Costenoble

Finite Mathematics & Applied Calculus: Pivot and Gauss Jordan Tool

For Students 9th - 10th
The learning tool investigates the Gauss-Jordan method. The tool performs row operations and reduces matrices.
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Showing That the Candidate Basis Does Span C(a)

For Students 9th - 10th
Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Example of Finding Matrix Inverse

For Students 9th - 10th Standards
A video lesson that works through a concrete example to find the inverse of a 3 x 3 matrix. The original matrix is augmented by the identity matrix and then put in reduced row echelon form. The result of the row operations on the...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Dimension of the Null Space or Nullity

For Students 9th - 10th
Video reviews how to find the null space of a matrix using reduced row echelon form. Shows that the vectors of the null space are linearly independent and form a basis for the null space. Extends this to show how the nullspace can be...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Null Space 2: Calculating the Null Space of Matrix

For Students 9th - 10th
Video demonstrates how to calculate the null space of a matrix by creating a system of equations and using reduced row echelon form to solve and represent the null space by a linear combination of vectors and by the span of vectors. This...

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