Matrices
Take your vector skills further by using matrices to transform the plane.
Vectors from Combinations
Possible Combinations
Standard Basis Vectors
Level Check
Transforming Vectors
Transforming Basis Vectors
Linear Transformations
Transforming Combinations
Plotting Transformed Vectors
Non-Integer Combinations
Level Check
Matrices as Transformations
Transforming via Matrices
Transforming Shapes
Diagonal Matrices
Rotations and Reflections
Shear Transformations
Degenerate Transformations
Matrix-Vector Multiplication
Matrix as Multiple Vectors
Matrix Addition and Subtraction
Scalar Matrix Multiplication
Matrix Multiplication
Matrix Dimensions
Sizing and Multiplying
The Identity Matrix
Multiple Transformations
Composing Transformations
Composing by Multiplying
Squaring and Cubing
Transformed Areas
Determinant of a Triangular Matrix
Determinant of any 2 by 2 Matrix
Computing Determinants
Determinant 0
Negative Determinants
The Inverse Matrix
Producing the Identity
Inverting a Matrix
Computing the Inverse Matrix
Non-invertible Matrices
Systems of Equations
Matrices as Systems of Equations
Solving Systems of Equations
Solving with Inverses
Course description
Discover what matrices really are by watching them transform the plane, with grids and basis vectors making every operation visual. By the end of the course, you'll be able to build a matrix for any linear transformation, multiply and compose them, compute determinants and inverses, and solve systems of equations. You'll see why matrix multiplication works the way it does instead of just memorizing the procedure.
Topics covered
- Composing Transformations
- Determinants
- Identity Matrix
- Inverse Matrices
- Linear Transformations
- Matrix Addition
- Matrix Dimensions
- Matrix Multiplication
- Scalar Multiplication
- Shears and Rotations
- Standard Basis Vectors
- Systems of Equations
Prerequisites and next steps
Before you get started, you should be comfortable working with vectors, including their components and how to write one vector as a linear combination of others, which you can pick up in the Vectors course. You don't need any prior experience with matrices to begin.