Mr. Integral

THE BIG IDEA

Vectors, Matrices and Systems

What does a system of equations look like geometrically?

Read a matrix equation both as constraints and as a combination of column vectors. Elimination exposes whether solutions exist and which choices remain free; factorizations make repeated solves manageable.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Column combinations
  2. resolving constraints uses02Elimination
  3. reusing elimination gives03Matrix factorization

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Vectors, Linear Combinations and SystemsRead a matrix equation as both a system of equations and a combination of its columns.
  2. 02Elimination, Pivots and Free VariablesReduce an augmented matrix and describe every solution, including inconsistent and underdetermined cases.
  3. 03Matrix Products, Inverses and LUInterpret matrix multiplication as composition and use factorization to solve systems efficiently.