Overview
On this page, you can find some useful resources which could help your learning process in your CEGEP Linear Algebra class - no matter which teacher you have or which textbook you use.
On this page, we start by looking at some basic facts about vectors and the operations we can do with them.
Important
The basic and advanced learning objectives listed below are meant to give you an idea of the material you should learn about this section. These are mainly intended to be used in a course which uses an Active Learning approach, where students are required to “read ahead” before each class - but can equally be used in a more traditional course setting.
Unless your teacher gives you specific instructions, it is up to you to decide how much of the listed resources you need to read or watch - you probably do not need to go through all of it. You might also want to look at the General Study Tips & Tricks page for some recommendations on how to effectively study with a math textbook and videos.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
-
Perform geometric operations on vectors: addition, subtraction, and multiplication by a scalar.
-
Perform algebraic operations on vectors: addition, subtraction, and multiplication by a scalar.
-
Determine whether two vectors are equivalent.
-
Determine whether two vectors are collinear.
-
Sketch vectors whose initial and terminal points are given, in 2-space.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
-
Sketch vectors whose initial and terminal points are given, in 3-space.
-
Solve geometric problems involving vectors.
-
Prove basic algebraic properties of vectors.
To prepare for class
-
Watch this introductory video by Grant Sanderson (“3Blue1Brown” on YouTube), explaining why the geometric & conceptual understanding of Linear Algebra is so important:
-
Watch this video by Grant Sanderson which gives a nice summary of (geometric and analytic) vectors, and the operations we can apply to them:
-
Watch this short video which explains how to find the vector coordinates of a vector between two points, and how to find its length (or “norm” or “magnitude”):
