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Définition d'un espace vectoriel
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines a real vector space through its eight axioms and discusses examples of sets with vector addition and scalar multiplication. Exercises ask students to test whether proposed structures are vector spaces.
- Vector space
- Vector space axiom
- Scalar multiplication
Matrices échelonnées et échelonnées réduites
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines row-echelon and reduced row-echelon forms, pivots, and pivot columns. Interactive exercises train students to identify echelon forms and apply elementary row operations.
- Row echelon form
- Reduced row echelon form
- Pivot
- Elementary row operation
Introduction aux équations et systèmes linéaires
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook introduces linear equations, systems of linear equations, and the definition of a solution. Through examples and exercises, students learn to recognize equations and verify solution sets.
- Linear equation
- System of linear equations
- Solution set
Notation matricielle des systèmes linéaires
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook rewrites systems of linear equations in the matrix form Ax=b and introduces coefficient and augmented matrices. Students practice matrix dimensions, vector notation, and the correspondence between equations and matrix entries.
- Matrix notation
- Augmented matrix
- System of linear equations
Résolution de systèmes linéaires
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook presents Gaussian elimination for solving systems from augmented matrices. It also distinguishes homogeneous and particular solutions and explains how free variables describe complete solution sets.
- Gaussian elimination
- Augmented matrix
- Homogeneous system
- Particular solution
Nombre de solutions d'un système linéaire
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook studies the three possible outcomes for a real linear system: no solution, one solution, or infinitely many solutions. Interactive examples and exercises help students interpret these cases geometrically and algebraically.
- System of linear equations
- Solution set
- Consistent system
Valeurs propres et vecteurs propres
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines eigenvalues and eigenvectors for linear transformations and square matrices. Examples and exercises train students to verify eigenpairs and interpret the invariant directions of a transformation.
- Eigenvalue
- Eigenvector
- Linear transformation
- Invariant direction