Linear Algebra
part 1 of 3

A total of 46 hours of lectures

This is an academic level course for university and college engineering. Due to its size, it is divided into three parts. This page describes the first of those three parts.

Prerequisites

High-school maths, mainly arithmetics, some trigonometry

Curriculum

Also make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

Linear Algebra, part 1 of 3

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Get the outline

A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.

Get Linear Algebra part 1 on Udemy

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Course Objectives & Outcomes for part 1

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How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
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Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).
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Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
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Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
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Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.
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Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
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Understand the connection between systems of linear equations and matrix multiplication.
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Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
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Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
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Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer’s rule for n-by-n systems of equations.
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Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
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Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
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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.
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Invertible Matrix Theorem and its applications; apply determinant test in various situations