This module looks at how matrices can be used to solve a system of equations and what our solutions tell us geometrically.
Systems of 2 equations – Smart Notebook – Introducing using matrices to solve a system of equations. Use autograph to further develop understanding.
Unique solutions – Powerpoint – Methods of solving a system of 3 equations where there is a unique solution.
Non-unique solutions – Powerpoint – 3 different cases and the geometry of these.
Investigation – Word – An investigation into how three planes can interact with each other.
Linear independence – Smart Notebook – What it means for a set of vectors to be linearly dependent/independent from each other.
Systems of equations revision notes – Word – An overview of the whole topic including worked examples.
Systems of 2 equations
Systems of 3 equations with unique solution using Gaussian elimination method
Linear Independence and Linear Dependence, Ex 1
Linear Independence and Linear Dependence, Ex 2
Determining If a Matrix is Consistent Using a Graphing Calculator