Lesson Plan: Rank of a Matrix: Determinants Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the rank of a matrix using determinants and how to use this to determine the number of solutions to a system of linear equations.
Objectives
Students will be able to
- find the rank of a matrix using determinants,
- recall how to relate a coefficient matrix and an augmented matrix to a system of linear equations,
- find the rank of an augmented matrix using determinants,
- find the number of solutions to a system of equations using the relationship between the rank of the coefficient matrix and the rank of the augmented matrix (Rouché–Capelli theorem).
Prerequisites
Students should already be familiar with
- augmented matrices,
- determinants,
- systems of equations.
Exclusions
Students will not cover
- row reduction.
