Algebra I Linear Systems

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

The EU is also introducing the basic language of polynomials.

Geometry of the plane and space:

• Points, vectors, translation by a vector, linear combinations, collinearity, independence, bases, reference frames and coordinates, change of reference frame, barycenters
• Straight lines and planes (without coordinates, then with coordinates), relative positions, intersections, equations
• Classical linear and affine transformations: homotheties, translations, symmetries, projections of the plane and space
• An introduction to 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 in^Rn, affine subspaces and vector subspaces of^Rn, parametric expressions and equations, sev generated by a family of vectors, sea generated by a point and a sev.
• Linear systems and pivot method: systems, solution sets, system matrix, echelon and reduced echelon systems, elementary operations, pivot method
• Matrix calculation: matrix operations, matrices of elementary row operations
• Linear applications of R², R³, and^{R^n}
• Matrix invertibility and the Gauss-Jordan method

Polynomials with real coefficients:

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

High school mathematics program (including plane and spatial geometry and equation solving), at least a specialization in the junior year and a specialization in mathematics in the senior year or an additional mathematics option.

Recommended prerequisites:

High school mathematics program (including plane and spatial geometry, and equation solving), ideally with a specialization in mathematics, or even an advanced mathematics option.

Hourly volumes:

            CM: 24 hours

            Tutorials: 25.5 hours

            TP: 0

            Land: 0