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# Cours scientifiques - FMA_1F001_EP : Linear Algebra

## Descriptif

Linear algebra (MAA101) is a fast-paced course which provides students with an overview of the most useful techniques of linear algebra. Upon completion of this course, students will fully understand the fundamental concepts of vector spaces, dimension, linear systems, matrices and determinants, and how they apply to problems in other elds of the Bachelor program.

Numérique sur 20

## Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

### Vos modalités d'acquisition :

This is a preliminary version: the teaching team will very likely change next year.

The exam and midterm are in open book format: all the documents available on Moodle are allowed during the exam and midterm. No other document is allowed.

The grade is computed as a mean of the exam (E), the midterm (M), 2 homeworks (H1 and H2) and shorts tests (T1 and T2). The formula is as follows:

Grade = (50/100)*max(E,(E+M)/2) + (15/100)T1 + (15/100)T2 + (10/100)H1 + (10/100)H2.

Le rattrapage est autorisé (Note de rattrapage conservée)
L'UE est acquise si Note finale >=
• Crédits ECTS acquis : 5 ECTS

La note obtenue rentre dans le calcul de votre GPA.

### Programme détaillé

Real and complex vector spaces, vector subspaces, direct sums of vector subspaces
Linear span, linear independence, bases, dimension
Linear maps, null-space, image, isomorphisms, image, linear forms, duality (elementary introduction)
Matrices and matrix calculus, matrix of a linear map, change of bases
Determinant of a matrix
Solving linear systems, geometric interpretation