Lecture

Column Rank and Systems of Equations

Description

This lecture covers the concept of column rank and its relation to systems of equations in linear algebra. It explains how to represent a system of equations using matrices, specifically the coefficient matrix and the augmented matrix. The lecture also delves into finding solutions for systems of equations by analyzing the column space of the coefficient matrix. Examples are provided to illustrate the concepts discussed, including determining the column rank and the dimension of the column space. Additionally, the lecture explores the relationship between the column space of a matrix and the solutions to the corresponding system of equations.

In MOOCs (9)
Algebra (part 1)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algebra (part 1)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algebra (part 2)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algebra (part 2)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Algebra (part 3)
Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.
Show more
Instructor
ad tempor
Adipisicing adipisicing minim minim laboris anim elit non eu culpa labore consectetur veniam do. Eiusmod quis dolor laborum in dolore duis non sit. Tempor nostrud reprehenderit fugiat ad occaecat mollit duis cupidatat irure non pariatur aute minim. Nisi est culpa nisi consequat enim elit deserunt quis cillum adipisicing. Reprehenderit est ipsum sunt exercitation ex ipsum dolore ad ad adipisicing magna duis. Esse do reprehenderit sit ut. Laborum pariatur aliqua in velit est fugiat.
Login to see this section
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (30)
Linear Equations: Vectors and Matrices
Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.
Matrix Similarity and Diagonalization
Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.
Matrix Operations: Definitions and Properties
Covers matrix operations, definitions, properties, and vector operations in Rn, essential for understanding linear algebra concepts.
Matrix Operations: Linear Systems and Solutions
Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.
Diagonalization of Matrices
Explores the diagonalization of matrices through eigenvectors and eigenvalues.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.