Vectors and Matrices
Master vector operations from addition and subtraction to linear combinations and polar form.
Vectors
Vector Addition
Drawing Vectors
Component-Wise Addition
Level Review
Opposite Vectors
Vector Subtraction
Drawing Differences
Vector Differences
Level Review
Scalar Multiplication
Reversing Direction
Linear Combinations
Linear Combination Grids
Solving Linear Combinations
Drawing Linear Combinations
Linear Interpolation
Level Review
Magnitude and Direction
Drawing from Polar Form
Polar Angles
Finding the Polar Angle
Computing from Components
Level Review
Vector Components
Non-Polar Angles
Combining Vectors
Level Review
Adding Velocities
Velocity Magnitude and Direction
Velocity from Bearing
Combining Velocity Bearings
Relative Velocity
Level Review
Scaling and Magnitude
Unit Vectors
Comparing Unit Vectors
The Dot Product
Unit Vector Dot Products
Level Review
General Dot Products
Scaling Dot Products
Dot Product from Magnitudes
Angle from Dot Product
Self Dot Products
Orthogonal Dot Products
Level Review
Vectors from Combinations
Possible Combinations
Standard Basis Vectors
Level Review
Transforming Vectors
Transforming Basis Vectors
Linear Transformations
Transforming Combinations
Plotting Transformed Vectors
Non-Integer Combinations
Level Review
Matrices as Transformations
Transforming via Matrices
Transforming Shapes
Diagonal Matrices
Rotations and Reflections
Shear Transformations
Degenerate Transformations
Level Review
Matrix-Vector Multiplication
Matrix as Multiple Vectors
Matrix Addition and Subtraction
Scalar Matrix Multiplication
Level Review
Matrix Multiplication
Matrix Dimensions
Sizing and Multiplying
The Identity Matrix
Level Review
Multiple Transformations
Composing Transformations
Composing by Multiplying
Squaring and Cubing
Level Review
Transformed Areas
Determinant of a Triangular Matrix
Determinant of any 2 by 2 Matrix
Computing Determinants
Determinant 0
Negative Determinants
Level Review
The Inverse Matrix
Producing the Identity
Inverting a Matrix
Computing the Inverse Matrix
Non-invertible Matrices
Level Review
Systems of Equations
Matrices as Systems of Equations
Solving Systems of Equations
Solving with Inverses
Level Review
Course description
First you'll learn to understand vectors as a shift in space, before learning to and and subtract them, work out their magnitude and direction, and break down vectors into their components.
Topics covered
- Vectors as a shift in space.
- Addition.
- Subtraction.
- Linear Combinations.
- Magnitude and Direction.
Prerequisites and next steps
Assumes knowledge of basic algebraic expressions and trigonometry.