# Lesson Plan: Properties of Determinants Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify the properties of determinants and use them to simplify problems.

#### Objectives

Students will be able to

- understand that the determinant of a matrix remains the same under transposition,
- understand that the determinant equals zero if a matrix includes a row (or column) of elements that are all equal to zero,
- understand that the determinant equals zero if a matrix has a repeated row (or column),
- understand that a common factor in the elements of any row (or column) in a matrix can be factored out of its determinant,
- understand that interchanging any two rows (or columns) of a matrix changes the sign of the determinant,
- understand the sum property of the determinants, which states that if all the elements of any row (or column) are written as a sum of two elements, then the value of the determinant can be expressed as a sum of two determinants,
- understands the invariance property of determinants, which states that the determinant of a matrix remains the same under the operation ,
- understand that multiplying the elements of any row (or column) of a matrix by the cofactors of the corresponding elements in another row (or column) will equal zero,
- understand that the determinant of an upper or lower triangular matrix is the product of the diagonal entries,
- understand that the determinant of a diagonal matrix is the product of the diagonal entries,
- determine the value of an unknown element or unknown variable in a matrix using the properties of determinants.

#### Prerequisites

Students should already be familiar with

- notation for matrix determinants,
- scalar multiplication of matrices,
- matrix transposition.

#### Exclusions

Students will not cover

- matrix multiplication,
- matrices and determinants larger than .