# Complete Quick Lessons on Linear Algebra

### Course Description

Patrick offers a series of 58 short lectures covering everything you need to know for elementary linear algebra. His lectures are well organized, and straight to the point. You will find it to be a great review for classes and exams.

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### Video Lectures & Study Materials

# Lecture Play Lecture
1 The Span of a Set of Vectors (17:06) Play Video
2 Determinants to Find the Area of a Polygon (3:35) Play Video
3 Determinants to Find the Area of a Triangle (2:44) Play Video
4 Solving a 3 x 3 System of Equations Using the Inverse (9:01) Play Video
5 Determinant of a 2 x 2 Matrix - A Few Basic Questions (2:45) Play Video
6 Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3 (5:28) Play Video
7 Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2 (7:14) Play Video
8 Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1 (6:46) Play Video
9 Cramer's Rule to Solve a System of 3 Linear Equations - Example 2 (9:39) Play Video
10 Cramer's Rule to Solve a System of 3 Linear Equations - Example 1 (10:50) Play Video
11 Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2 (5:37) Play Video
12 Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1 (7:12) Play Video
13 Solving a Dependent System of Linear Equations involving 3 Variables (9:46) Play Video
14 Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3 (3:03) Play Video
15 Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2 (4:02) Play Video
16 Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1 (3:43) Play Video
17 Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3 (8:18) Play Video
18 Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2 (4:15) Play Video
19 Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1 (6:46) Play Video
20 Finding the Determinant of a 3 x 3 matrix (6:56) Play Video
21 Row Reducing a Matrix - Systems of Linear Equations - Part 2 (5:35) Play Video
22 Row Reducing a Matrix - Systems of Linear Equations - Part 1 (10:00) Play Video
23 Solving Systems of Equations Using Elimination By Addition (10:00) Play Video
24 Multiplying Matrices - Example 1 (9:38) Play Video
25 Matrix Operations (5:25) Play Video
26 Orthogonal Projections - Scalar and Vector Projections (3:21) Play Video
27 An Introduction to the Dot Product (4:06) Play Video
28 Sketching Sums and Differences of Vectors (3:22) Play Video
29 Word Problems Involving Velocity or Other Forces (Vectors), Ex 3. (2:10) Play Video
30 Word Problems Involving Velocity or Other Forces (Vectors), Ex 2 (11:29) Play Video
31 Word Problems Involving Velocity or Other Forces (Vectors), Ex 1 (3:10) Play Video
32 Finding a Unit Vector, Ex 2 (4:55) Play Video
33 Finding a Unit Vector, Ex 1 (2:07) Play Video
34 Finding the Components of a Vector, Ex 2 (6:34) Play Video
35 Finding the Components of a Vector, Ex 1 (2:38) Play Video
36 Vector Addition and Scalar Multiplication, Example 2 (3:52) Play Video
37 Vector Addition and Scalar Multiplication, Example 1 (3:24) Play Video
38 Magnitude and Direction of a Vector, Example 3 (6:05) Play Video
39 Magnitude and Direction of a Vector, Example 2 (3:46) Play Video
40 Magnitude and Direction of a Vector, Example 1 (3:58) Play Video
41 When Are Two Vectors Considered to Be the Same? (2:03) Play Video
42 An Introduction to Vectors, Part 1 (4:46) Play Video
43 Finding the Vector Equation of a Line (7:41) Play Video
44 Vector Basics - Algebraic Representations Part 2 (5:35) Play Video
45 Vector Basics - Algebraic Representations (6:16) Play Video
46 Vector Basics - Drawing Vectors/ Vector Addition (11:32) Play Video
47 Vectors - The Dot Product (7:27) Play Video
48 Vectors - Finding Magnitude or Length (3:33) Play Video
49 Linear Independence and Linear Dependence, Ex 2 (6:46) Play Video
50 Linear Independence and Linear Dependence, Ex 1 (8:05) Play Video
51 Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2 (10:33) Play Video
52 Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1 (9:09) Play Video
53 Useful Things to Remember About Linearly Independent Vectors (4:41) Play Video
54 Basis for a Set of Vectors (11:44) Play Video
55 Useful Things to Remember About Linearly Independent Vectors (4:41) Play Video
56 Procedure to Find a Basis for a Set of Vectors (7:17) Play Video
57 Linear Transformations , Example 1, Part 2 of 2 (4:56) Play Video
58 Linear Transformations , Example 1, Part 1 of 2 (9:06) Play Video