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Matrices ... What are they?
What is a matrix?
A matrix is a useful way of representing linear relationships between variables.
Matrices look like grids or tables with lists of numbers written in rows and columns.

This matrix has 2 horizontal lists of numbers called rows. 

This matrix has 3 vertical lists of numbers called columns. 
Each element appears at the intersection between a row and a column.

This matrix has 6 elements. 

This element is in row 2 and column 3. 
Converting a twoway table into a matrix
The data in the table below shows that, in a group of 50 children, 5 girls have cats as pets, 17 girls have dogs as pets, 3 boys have cats as pets and 25 boys have dogs as pets.
Pets  ... and here is its corresponding matrix  



Gender 

5  17  

3  25 
Types of matrices
Row matrices  * one row only  
Column matrices  * one column only  
Square matrices  * number of rows = number of columns  
Identity matrices 
* 1s on the leading diagonal * 0s elsewhere 

Diagonal matrices 
* any numbers on the leading diagonal * 0s elsewhere 

Zero matrices  * all elements are 0s  
Upper triangular matrices  * all elements below the leading diagonal are 0s  
Lower triangular matrices  * all elements above the leading diagonal are 0s 
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