In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices. Given the matrices A and B, where the augmented matrix (A|B) is written as This is useful when solving systems of linear equations. For a given number of unknowns, the number of solutions to a system of linear equations depends only on the rank of the matrix representing the system and the rank of the corresponding augmented matrix. Specifically, according to the Rouché–Capelli theorem, any system of linear equations is inconsistent (has no solutions) if the rank of the augmented matrix is greater than the rank of the coefficient matrix; if, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution. The solution is unique if and only if the rank equals the number of variables. Otherwise the general solution has k free parameters where k is the difference between the number of variables and the rank; hence in such a case there are an infinitude of solutions. An augmented matrix may also be used to find the inverse of a matrix by combining it with the identity matrix. (Wikipedia).
Introduction to Augmented Matrices
This video introduces augmented matrices for the purpose of solving systems of equations. It also introduces row echelon and reduced row echelon form. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Augmented Matrices
Solve a System of 3 Equations with 3 Unknowns Using an Augmented Matrix (RREF - 1 Solution)
This video provides an example of how to solve a system of equations using an augmented matrix.
From playlist Augmented Matrices
Ex: Give the Solution From an Augmented Matrix in RREF (3x3)
This video explains how to determine the solution to a system of equations from an augmented matrix in reduced row echelon form. http://mathispower4u.com
From playlist Augmented Matrices
Use Elementary Matrices to Perform Row Operations to Solve a System
This video will explain how to find the elementary matrices that can be used to write an augmented matrix in echelon form to solve a system of equations. Site: mathispower4u.com Blog: mathispower4u.wordpress.com
From playlist Augmented Matrices
Ex 1: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
This video explains how to solve a system of equations by writing an augmented matrix in reduced row echelon form. This example has one solution. Site: http://mathispower4u.com
From playlist Augmented Matrices
Ex: Write a System of Equations as an Augmented Matrix (3x3)
This video explains how to write an augmented matrix for a system of three equations with three unknowns. http://mathispower4u.com
From playlist Augmented Matrices
Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
This video provides an example of how to solve a system of two linear equations with two unknowns by writing an augmented matrix in row echelon form. This example has one solution. Site: http://mathispower4u.com
From playlist Augmented Matrices
8.1/9.1 Definition of Matrix and Augmented Matrix
MATH 1314 Kilgore College
From playlist MATH 1314: College Algebra (depreciated)
Solve a 3x3 System Using an Augmented Matrix (RREF on Desmos Matrix Calc)
This video explains how to solve a system of linear equations by writing an augmented matrix in reduced row echelon form using the Desmos matrix calculator.
From playlist Augmented Matrices
(3.2.4A) Solving a System of Linear Equations Using an Augmented Matrix
This lesson explains how to solve a system of equations using an augmented matrix. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Solve a 2x2 System Using an Augmented Matrix (RREF on Desmos Matrix Calc)
This video explains how to solve a system of linear equations by writing an augmented matrix in reduced row echelon form using the Desmos matrix calculator.
From playlist Augmented Matrices
This video covers the second half of Chapter 1.1. It goes from Example 2 to the Worksheet. These videos are associated the textbook by Scott Stevens entitled Matrices, Vectors, & 3D Math; A Game-Programming approach with MATLAB (http://www.StevensMV3D.com).
From playlist Matrices, Vectors, & 3D Math: Lecture Videos
Solving Systems of Linear Equations — Abstract Linear Algebra 17
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From playlist Abstract Linear Algebra
Intro to Matrices and Linear Systems
How to write a linear system as a matrix equation. What is an augmented matrix? Why are matrices important? These questions will be addressed in this introductory video.
From playlist Intro to Linear Systems
Solve a System of Equations Using an Augmented Matrix RREF: Burger App (Desmos)
This video explains in to set-up a system of equations to solve an application. The desmos is used to write the augmented matrix in reduced row echelon form.
From playlist Augmented Matrices
Determine Which Sets of 3 Vectors Form a Basis for R3 (Independence and Span Test)
This video explains how to determine if a set of 3 vectors form a basis for R3.
From playlist Linear Independence and Bases
Augmented Matrices: Row Echelon Form
This video shows how to transform and augmented matrix to row echelon form to solve a system of equations. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Augmented Matrices