# Determinants, Objectives, Determinant of Order 2, Expansion of a Determination of Order 2, Determinant of Order 3

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## Objectives

After studying this lesson, you will be able to:

## Determinant of Order 2

Let us consider the following system of linear equations:

On solving this system of equations for and , we get

and provided

The number determines whether the values of and exist or not.

The number is called the value of the determinant, and we write

i.e. belongs to the row and column

belongs to the row and column

belongs to the row and column

belongs to the row and column

## Expansion of a Determination of Order 2

A formal rule for the expansion of a determinant of order 2 may be stated as follows: In the determinant,

Multiply the elements by the arrow. The sign of the arrow going downwards is positive, i.e., and the sign of the arrow going upwards is negative, i.e.,

Add these two products, i.e., or which is the required value of the determinant.

Example:

Evaluate:

(1) (2)

Solution:

(1)

(2)

## Determinant of Order 3

The expression contains nine quantities arranged in rows and columns, is called determinant of order . (Or a determinant of third order). A determinant of order has elements.

Using double subscript notations, viz, for the elements .

We write a determinant of order3 as follows:

Usually a determinant, whether of order or , is denoted by or etc.

, where and