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Determinants and Systems of Linear Equations — Part 1: Determinants, properties and area

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Lesson

Determinants and Systems of Linear Equations, Part 1

A single number that tells you whether a square matrix can be undone.

In this lesson you will

Evaluate determinants of order two and three by expansion
Find minors and cofactors and use them in expansions
Use properties of determinants to simplify, prove identities and solve equations
Find the area of a triangle and test collinearity with determinants

Part 1 at a glance.

Concept

What you will learn

Value of a determinant of order 2 and 3
Minors and cofactors
Properties of determinants
Area and collinearity

Four skills for Part 1.
You will learn to	Topic
evaluate determinants of order $2$ and $3$	expansion
find minors and cofactors	cofactors
use row and column operations instead of long expansion	properties
find areas and test collinearity	coordinate geometry

Concept

Determinant of order two

$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$ .

Leading diagonal product minus the other diagonal product.
Determinant	Rule	Value
$\begin{vmatrix} 6 & -1 \\ 4 & 3 \end{vmatrix}$	$(6)(3) - (-1)(4)$	$22$
$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$	$ad - bc$	—