Matrices | Mathematics Form 3

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Matrices - Mathematics Form 3

There are various situations where data can be organized in a rectangular or square pattern to make it easy to do basic arithmetic operations. Such patterns can be used in real life situations. The following shows two types of patterns and how one can form patterns from real life situations.

a) Rectangular pattern with 3 rows and 4 columns

X X X X
X X X X
X X X X

b) Square pattern 3 rows and 3 columns

X X X
X X X
X X X


Example

John and Mary are two shopkeepers. On Monday John sold 2 sodas and 4 cakes, while Mary sold 1 soda and 6 cakes. On Tuesday, John sold 3 sodas and 5 cakes, while Mary sold 3 soda and 8 cakes. The cost of a soda is Ksh. 20, while that of a cake is Ksh. 10.
Form a pattern for:
I. Number of items sold.
II. Price of the items.

Solution




 




MATRICES

In life, we encounter activities that require organisation of data in a tabular form.For example, a sales person sold cakes, sodas and loaves of bread in three days of a week and recorded the information as shown below.

The data can be used to calculate the amount of money obtained from the sales if given the prices of each item.



Order of a matrix
A matrix is described by its order i.e. the number of rows and the number of columns a matrix has. If the order of a matrix is written as 2 x 3 it is read as a two by three matrix. This means it has two rows and three columns.
Example 1
The order of the matrix A given below is four by three meaning that it has
four rows and three columns.

Example 2
The order of the matrix B given below is three by two meaning
it has three rows and two columns

Example 3
The matrix (2 0 1 5) is a matrix of order 1 x 4, and is also refered to as a 1 x 4 matrix, since it has one row and four columns.

Note:
This matrix has only one row. Such a matrix with only one row is called a row matrix.

Example 4


This is a matrix of order 5 x 1, also refered to as a 5 x 1 matrix, since it has 5 rows and 1 column.

Note:
This matrix has only one column. Such a matrix with one column is called a column matrix.



Example 5

This is a matrix of order 2 x 2 ,also known as a 2 x 2 matrix.

It has 2 rows and 2 columns. Here the number of rows is equal to the number of columns. Such a matrix which has equal number of rows and columns is called a square matrix.



We can work out the total price of the biscuits as follows

(40 x 200) + (150 x 65) + (300 x 80) + (250 x 75) = shs.43,500

The quantity can be written in matrix form as a row matrix or a column matrix as follows:

The price can also be written as a row or a column matrix as follows:


We can find the total costs of the biscuits by multiplying the above matrices.This is done by writing the first matrix as a row matrix and the second as a column matrix and finding the product of the matrices as follows:


Similarly,

Therefore, 1 x 4 matrix multiplied by a 4x1 matrix gives a 1x1 which is (43, 500)

.

NOTE:
Two matrices can be multiplied only if they are compatible. Matrices are said to be compatible for multiplication if the number of columns in the left matrix equals to the number of rows in the right matrix.









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