This course on Linear Algebra aims to teach students the fundamentals of vectors, vector operations, vector properties, and dot products. By the end of the course, students will be able to calculate vector lengths, perform vector operations, understand the properties of vectors, and calculate dot products. The teaching method involves theoretical explanations followed by practical examples. This course is intended for learners interested in gaining a foundational understanding of linear algebra concepts.
Overview
Syllabus
Introduction to Vectors.
Length of a Vector in 2 Dimensions (examples).
1.1 Vector Addition.
1.1 Multiplying a Vector by a Scalar.
1.1 Vector Subtraction.
1.1 Vectors with 3 components (3 dimensions).
1.1 Length of a 3-Dimensional Vector.
1.1 Definition of R^n.
1.1 Length of a Vector.
1.2 Proof: Vector Addition is Commutative and Associative.
1.2 Algebraic Properties of Vectors.
1.3 Definition of the Dot Product.
1.3 Dot Product - Angle Between Two Vectors.
1.3 Find the Angle Between Two Vectors (example).
1.3 Orthogonal Vectors.
1.3 Proof about the Diagonals of a Parellelogram.
Taught by
rootmath
