Linear Algebra and Geometry 1
Systems of equations, matrices, determinants, vectors, and geometry of straight lines and planes in the 3-space
4.86 (975 reviews)
7,862
students
47 hours
content
Apr 2025
last update
$89.99
regular price
What you will learn
How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).
Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer's rule for n-by-n systems of equations.
Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.
Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.
Understand the connection between systems of linear equations and matrix multiplication.
Invertible Matrix Theorem and its applications; apply determinant test in various situations.
Screenshots
Related Topics
4025832
udemy ID
5/4/2021
course created date
5/20/2021
course indexed date
Bot
course submited by