Lessons
Eight short lessons, in order. Each one explains a single idea, works through an example, then lets you try it yourself.
- Lesson 1: What is a vector? A vector is an ordered list of numbers. Learn to read its components and draw it as an arrow. Skills: read a component, read a vector from a picture, equal vectors.
- Lesson 2: Add and subtract vectors Combine two vectors by adding or subtracting their matching components. Skills: add two vectors, subtract two vectors.
- Lesson 3: Multiply a vector by a number Stretch, shrink or flip a vector by multiplying every component by a scalar. Skills: multiply a vector by a number.
- Lesson 4: What is a matrix? A matrix is a rectangle of numbers. Learn rows, columns, size and how to name one entry. Skills: size of a matrix, read an entry.
- Lesson 5: Add and subtract matrices Add or subtract two matrices of the same size, one position at a time. Skills: add two matrices, subtract two matrices.
- Lesson 6: Multiply a matrix by a number Multiply every entry of a matrix by the same scalar. Skills: multiply a matrix by a number.
- Lesson 7: Transpose a matrix Swap rows and columns, and see why the size of a matrix can change. Skills: transpose a matrix.
- Lesson 8: Dot product basics Multiply matching components and add: two vectors in, one number out. Skills: dot product.
- Optional: matrix times vector An optional next step: use dot products to multiply a 2×2 matrix by a vector. Skills: matrix times vector.