Algebra I linear systems

This UE is an introduction to linear algebra (formalized in S2), based on intuition from plane and space geometry. It includes an introduction to matrix calculus.

The UE also introduces the basic language of polynomials.

Plane and space geometry :

• Points, vectors, translation by a vector, linear combinations, collinearity, independence, bases, reference points and coordinates, change of reference point, barycenters
• Lines and planes (without coordinates then with), relative positions, intersections, equations
• Classical linear and affine transformations: homotheties, translations, symmetries, projections of the plane and space
• A foray into Euclidean geometry: scalar product, orthogonality, distance, vector product, orthonormal bases and reference frames, orthogonal projections, distance from a point to a line/plane.

Linear algebra in R², R³ and ^Rn:

• Points and vectors of ^Rn, affine subspaces and vector subspaces of ^Rn, parametric expression and equations, sev generated by a family of vectors, sea generated by a point and a sev.
• Linear systems and pivot method: systems, sets of solutions, matrix of a system, staggered and reduced staggered systems, elementary operations, pivot method
• Matrix calculation: operations on matrices, matrices of elementary operations on rows
• Linear applications of R², R³ and ^Rn
• Matrix reversibility and the Gauss-Jordan method

Polynomials with real coefficients :

• Definitions of a polynomial and a polynomial function, links
• Coefficients, degree, roots, operations
• Factoring and Euclidean division of polynomials
• Multiplicity of roots, link to derivative, Taylor formula for polynomials

High school mathematics curriculum (including plane and space geometry, and equation solving), at least first year specialization and final year mathematics specialization or complementary mathematics option.

Recommended prerequisites* :

High school mathematics curriculum (including plane and space geometry, and equation solving), ideally specializing in mathematics, or even expert mathematics.

Hourly volumes* :

            CM : 24 h

            TD: 25.5 h

            TP: 0

            Land: 0