Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Linear Systems: Solutions and Compatibility

In course

MATH-111(f): Linear Algebra

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications. ...

Description

This lecture introduces the concept of compatibility in linear systems, defining solutions as lists that satisfy the system's equations. It explores methods to determine the number of solutions and the importance of triangular systems for easy solving.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Mikaël Cavallin

Official source

Related concepts (10)

Backward compatibility

Backward compatibility (sometimes known as backwards compatibility) is a property of an operating system, software, real-world product, or technology that allows for interoperability with an older legacy system, or with input designed for such a system, especially in telecommunications and computing. Modifying a system in a way that does not allow backward compatibility is sometimes called "breaking" backward compatibility. Such breaking usually incurs various types of costs, such as switching cost.

Computer compatibility

A family of computer models is said to be compatible if certain software that runs on one of the models can also be run on all other models of the family. The computer models may differ in performance, reliability or some other characteristic. These differences may affect the outcome of the running of the software. Software compatibility can refer to the compatibility that a particular software has running on a particular CPU architecture such as Intel or PowerPC.

Binary-code compatibility

Binary-code compatibility (binary compatible or object-code-compatible) is a property of a computer system, meaning that it can run the same executable code, typically machine code for a general-purpose computer CPU, that another computer system can run. Source-code compatibility, on the other hand, means that recompilation or interpretation is necessary before the program can be run on the compatible system.

Elementary matrix

In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form.

Source-code compatibility

Source-code compatibility (source-compatible) means that a program can run on computers (or operating systems), independently of binary-code compatibility and that the source code is needed for portability. The source code must be compiled before running, unless the computer used has an interpreter for the language at hand. The term is also used for assembly language compatibility, where the source is a human-readable form of machine code that must be converted into numerical (i.e. executable) machine code by an assembler.

Related lectures (31)

Linear Systems: Fundamentals and Applications

Explores the power of linear systems in control theory and data science.

Factorisation LU

Explains Gaussian elimination and LU factorization for solving linear systems of equations.

Linear Systems Resolution MOOC: Warm-up for EPFL MOOC: Linear Algebra (Part 1)

Covers the resolution of linear systems using the Gauss method to determine unique, infinite, or no solutions.

Equilibrium Extension Analysis

Discusses equilibrium, extension analysis, stress distribution, and strain components' compatibility for a valid solution.

Calcul du pi1 de XUCA