Useful Things to Remember About Linearly Independent Vectors
by
Patrick JMT

### Lecture Description

Useful Things to Remember About Linearly Independent Vectors. Just a few things that I think are useful to remember about linearly independent and dependent sets of vectors!

### Course Index

- The Span of a Set of Vectors
- Determinants to Find the Area of a Polygon
- Determinants to Find the Area of a Triangle
- Solving a 3 x 3 System of Equations Using the Inverse
- Determinant of a 2 x 2 Matrix - A Few Basic Questions
- Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 3
- Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2
- Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1
- Cramer's Rule to Solve a System of 3 Linear Equations - Example 2
- Cramer's Rule to Solve a System of 3 Linear Equations - Example 1
- Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2
- Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1
- Solving a Dependent System of Linear Equations involving 3 Variables
- Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 3
- Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 2
- Systems of Linear Equations - Inconsistent Systems Using Elimination by Addition - Example 1
- Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 3
- Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 2
- Solving a System of Equations Involving 3 Variables Using Elimination by Addition - Example 1
- Finding the Determinant of a 3 x 3 matrix
- Row Reducing a Matrix - Systems of Linear Equations - Part 2
- Row Reducing a Matrix - Systems of Linear Equations - Part 1
- Solving Systems of Equations Using Elimination By Addition
- Multiplying Matrices - Example 1
- Matrix Operations
- Orthogonal Projections - Scalar and Vector Projections
- An Introduction to the Dot Product
- Sketching Sums and Differences of Vectors
- Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.
- Word Problems Involving Velocity or Other Forces (Vectors), Ex 2
- Word Problems Involving Velocity or Other Forces (Vectors), Ex 1
- Finding a Unit Vector, Ex 2
- Finding a Unit Vector, Ex 1
- Finding the Components of a Vector, Ex 2
- Finding the Components of a Vector, Ex 1
- Vector Addition and Scalar Multiplication, Example 2
- Vector Addition and Scalar Multiplication, Example 1
- Magnitude and Direction of a Vector, Example 3
- Magnitude and Direction of a Vector, Example 2
- Magnitude and Direction of a Vector, Example 1
- When Are Two Vectors Considered to Be the Same?
- An Introduction to Vectors, Part 1
- Finding the Vector Equation of a Line
- Vector Basics - Algebraic Representations Part 2
- Vector Basics - Algebraic Representations
- Vector Basics - Drawing Vectors/ Vector Addition
- Vectors - The Dot Product
- Vectors - Finding Magnitude or Length
- Linear Independence and Linear Dependence, Ex 2
- Linear Independence and Linear Dependence, Ex 1
- Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2
- Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1
- Useful Things to Remember About Linearly Independent Vectors
- Basis for a Set of Vectors
- Useful Things to Remember About Linearly Independent Vectors
- Procedure to Find a Basis for a Set of Vectors
- Linear Transformations , Example 1, Part 2 of 2
- Linear Transformations , Example 1, Part 1 of 2

### 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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