## Linear Algebra - Lecture 25 - The Invertible Matrix Theorem

In this lecture, we discuss The Invertible Matrix Theorem, which is a list of 12 equivalent statements that classify when a square matrix is invertible....

From James Hamblin

In this lecture, we discuss The Invertible Matrix Theorem, which is a list of 12 equivalent statements that classify when a square matrix is invertible....

From James Hamblin

In this lecture, we discuss The Invertible Matrix Theorem, which is a list of 12 equivalent statements that classify when a square matrix is invertible....

From James Hamblin

In this video, we will discuss elementary matrices and their relationship to invertible matrices. We will prove a theorem that explains how to tell when a matrix is invertible, and how to find the inverse of an invertible matrix....

From James Hamblin

In this video, we will discuss elementary matrices and their relationship to invertible matrices. We will prove a theorem that explains how to tell when a matrix is invertible, and how to find the inverse of an invertible matrix....

From James Hamblin

In this lecture, we'll learn about the multiplicative inverse of a matrix. We'll discuss inverses of 2x2 matrices, as well as properties of inverses....

From James Hamblin

In this lecture, we'll learn about the multiplicative inverse of a matrix. We'll discuss inverses of 2x2 matrices, as well as properties of inverses....

From James Hamblin

In this lecture, I'll discuss the algebraic properties of matrix multiplication. We'll talk about proving some of the properties, and work through several examples....

From James Hamblin

In this lecture, I'll discuss the algebraic properties of matrix multiplication. We'll talk about proving some of the properties, and work through several examples....

From James Hamblin

In this lecture we will discuss matrix operations. Specifically, we will define matrix addition, multiplying a matrix by a scalar, and matrix multiplication....

From James Hamblin

In this lecture we will discuss matrix operations. Specifically, we will define matrix addition, multiplying a matrix by a scalar, and matrix multiplication....

From James Hamblin

In this lecture, we will investigate the "onto" and "one-to-one" function properties, and how these apply to linear transformations....

From James Hamblin

In this lecture, we will investigate the "onto" and "one-to-one" function properties, and how these apply to linear transformations....

From James Hamblin

In this lecture, we will learn that every linear transformation is a matrix transformation....

From James Hamblin

In this lecture, we will learn that every linear transformation is a matrix transformation....

From James Hamblin

In this lecture, we will generalize the ideas about matrix transformations and define linear transformations....

From James Hamblin

In this lecture, we will generalize the ideas about matrix transformations and define linear transformations....

From James Hamblin

In this lecutre, we will discuss matrix transformations, which are functions that arise from multiplying a matrix by a vector. We will establish some vocabulary that we will be using when discussing these types of functions....

From James Hamblin

In this lecutre, we will discuss matrix transformations, which are functions that arise from multiplying a matrix by a vector. We will establish some vocabulary that we will be using when discussing these types of functions....

From James Hamblin

In this lecture, we will start proving some theorems that let us characterizing when a set of vectors is linearly dependent or linearly independent....

From James Hamblin

In this lecture, we will start proving some theorems that let us characterizing when a set of vectors is linearly dependent or linearly independent....

From James Hamblin

In this lecture, we learn the definition of linear independence and linear dependence. We work through several examples to illustrate the definitions....

From James Hamblin

In this lecture, we learn the definition of linear independence and linear dependence. We work through several examples to illustrate the definitions....

From James Hamblin

In this lecture, we study how to apply linear algebra techniques to flow networks....

From James Hamblin

In this lecture, we study how to apply linear algebra techniques to flow networks....

From James Hamblin

In this lecture, we learn how to use linear algebra to balance chemical equations....

From James Hamblin

In this lecture, we learn how to use linear algebra to balance chemical equations....

From James Hamblin

In this lecture, we study how to use linear algebra to solve input-output problems in economics....

From James Hamblin

In this lecture, we study how to use linear algebra to solve input-output problems in economics....

From James Hamblin

In this lecture, we express the solution set of non-homogeneous linear systems in terms of the corresponding homogeneous system....

From James Hamblin

In this lecture, we express the solution set of non-homogeneous linear systems in terms of the corresponding homogeneous system....

From James Hamblin

In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form....

From James Hamblin

In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form....

From James Hamblin

In this lecture, we define the product of a matrix by a vector. We also discuss matrix equations and their connection to systems of linear equations and vector equations....

From James Hamblin

In this lecture, we define the product of a matrix by a vector. We also discuss matrix equations and their connection to systems of linear equations and vector equations....

From James Hamblin

In this lecture, we discuss the idea of span and its connection to linear combinations. We also discuss the use of "span" as a verb, when a set of vectors "spans" the entire set R^n....

From James Hamblin

In this lecture, we discuss the idea of span and its connection to linear combinations. We also discuss the use of "span" as a verb, when a set of vectors "spans" the entire set R^n....

From James Hamblin

In this lecture, we discuss linear combinations and vector equations....

From James Hamblin

In this lecture, we discuss linear combinations and vector equations....

From James Hamblin

In this lecture, we discuss vectors (also called "column vectors") and related operations....

From James Hamblin

In this lecture, we discuss vectors (also called "column vectors") and related operations....

From James Hamblin

In this lecture, we discuss how to interpret the echelon or reduced echelon form of a matrix. What does the echelon form tell us about the solutions to the corresponding system of linear equations?...

From James Hamblin

In this lecture, we discuss how to interpret the echelon or reduced echelon form of a matrix. What does the echelon form tell us about the solutions to the corresponding system of linear equations?...

From James Hamblin

In this lecture, we discuss the process for using row operations to find an echelon or reduced echelon form for a given matrix. This process is also sometimes called Gaussian elimination....

From James Hamblin

In this lecture, we discuss the process for using row operations to find an echelon or reduced echelon form for a given matrix. This process is also sometimes called Gaussian elimination....

From James Hamblin

In this lecture, we define the "echelon form" and "reduced echelon form" of a matrix. We focus on defining the forms and determining whether a matrix is in the form....

From James Hamblin

In this lecture, we define the "echelon form" and "reduced echelon form" of a matrix. We focus on defining the forms and determining whether a matrix is in the form....

From James Hamblin

In this lecture, we discuss the substitution and elimination methods for solving a system of linear equations....

From James Hamblin

In this lecture, we discuss the substitution and elimination methods for solving a system of linear equations....

From James Hamblin