# Course curriculum

• 1

### Introduction to Linear Algebra

• Introduction to Linear Algebra

• Linear Algebra Applications

• Linear Combination and Linear Equations

• Quiz 1 - Linear Combination and Linear Equations

• System of Linear Equations

• Solution of Linear Systems - Elementary Methods

• Quiz 2 - System of Linear Equations

• Linear System Examples

• Feedback

• 2

### Vectors

• What are Vectors?

• Basic Operations on Vectors

• Quiz 3 - Basic Operations on Vectors

• Interconversion between Polar and Rectangular Coordinates

• Quiz 4 - Rectangular and Polar Coordinates

• Norm of a Vector

• Dot Product

• Applications of Dot Product

• Quiz 5 - Dot Product and Norm of a Vector

• Linear Combination of Vectors

• Span and Linear Independence

• Quiz 6 - Linear Combination and Span of Vectors

• Feedback

• 3

### Matrices

• System of Linear Equations and Matrices

• Matrices Origin and Evolution

• Basic Operations and Properties

• Quiz 7 - Basic Operations on Matrices

• Linear Transformation - Part 1 - Geometry and Intuition

• Linear Transformation - Part 2 - Common Transformations

• Linear Transformation - Part 3 - Mathematics of Linear Transformation

• Composition of Transformations

• Quiz 8 - Matrix Multiplication and Linear Transformation

• Determinants

• Quiz 9 - Determinants

• Solution of Equations - Cramer's Rule

• Solution of Equations - Matrix Inverse

• Quiz 10 - Matrix Inverse

• Reduced Row Echelon Form - RREF

• Solution of Equations - RREF

• Quiz 11 - Reduced Row Echelon Form

• Eigenvalues and Eigenvectors

• Eigenvalues and Eigenvectors - 3 x 3 Systems

• Quiz 12 - Eigenvalues and Eigenvectors

• Feedback

• 4

### Congratulations! You have successfully completed this course!

• Congratulations!