A system of linear equations has 3 possibilities concerning its solution: it may have several solutions, a unique solution, or no solution at all. the type of solution of the system depends essentially on its coefficients. In particular, if the coefficients of a system depend on one or more parameters, the type of solution may vary according to the values of the parameters, which constitutes an important mathematical phenomene.

Parmsys is therefore an exercise designed to help you understand this phenomenon concerning linear systems with parameters. The server will propose such a system to you, and then ask you to determine which conditions on the parameters lead to which type of solution.

The principal tool used to solve the problem is the method of Gauss elimination. Therefore, the exercise incorporates a user-friendly interface allowing you to simplify the system by the method of Gauss, before replying to the questions.

Choose a level of difficulty suitable for you: 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 .

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Description: analyse a linear system with parameters, using Gauss elimination. exercises interactifs, calcul et tracé de graphes en ligne

Keywords: interactive mathematics, interactive math, server side interactivity, algebra, linear_algebra, gauss_algorithm, linear_systems