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.
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This matrix has 2 horizontal lists of numbers called rows. |
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This matrix has 3 vertical lists of numbers called columns. |
Each element appears at the intersection between a row and a column.
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This matrix has 6 elements. |
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This element is in row 2 and column 3. |
Converting a two-way 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 |
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| Gender |
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5 | 17 | ||
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3 | 25 | |||
Types of matrices
| Row matrices | * one row only |
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| Column matrices | * one column only |  |
| Square matrices | * number of rows = number of columns |  |
| Identity matrices |
* 1s on the leading diagonal * 0s elsewhere |
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| Diagonal matrices |
* any numbers on the leading diagonal * 0s elsewhere |
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| Zero matrices | * all elements are 0s |
 
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| Upper triangular matrices | * all elements below the leading diagonal are 0s |  |
| Lower triangular matrices | * all elements above the leading diagonal are 0s |  |