##
__Creating the 3x3 matrix__

To create a 3x3 matrix, begin with an array

```
$a = array(array(1,5,7),array(7,3,5),array(2,6,9));
$rows = count($a);
$cols = count($a[0]);
for ($k = 0; $k < $rows; $k++){
for ($j = 0; $j < $cols; $j++){
echo ($a[$k][$j]." ");
}
echo ("<br>");
}
```

This will result in

```
1 5 7
7 3 5
2 6 9
```

##
__Getting 2x2 matrices__

__Getting 2x2 matrices__

There are 4 possible 2x2 matrices that could be derived from the 3x3 matrix above.

Begin with row index zero and column index zero and reduce the number of rows and columns by one. (since its a 3x3 matrix we wish to reduce to a 2x2, the row and column both reduce by one)

To create another matrix, Increment either the row by one. Repeat this step with the column, this time holding the row constant.

The first 2x2 matrix is begins at k = 0 and j = 0. However, the arrays are reduced by one from both ends like seen in the code:

```
for ($k = 0; $k < $rows-1; $k++){
for ($j = 0; $j < $cols-1; $j++){
echo ($a[$k][$j]." ");
}
echo ("<br>");
}
```

The output of this is:

```
1 5
7 3
```

The maximum and minimum values of this matrix are 7 and 1 respectively.

The second 2x2 matrix has the row starting at k=0 and ending at k < row-1 but the column starts at j =1 and ends at j < cols as shown below:

```
for ($k = 0; $k < $rows-1; $k++){
for ($j = 1; $j < $cols; $j++){
echo ($a[$k][$j]." ");
}
echo ("<br>");
}
```

The output of this is:

```
5 7
3 5
```

The maximum and minimum values of this matrix are 7 and 3 respectively.

Here, the rows start at k =1 while the columns start at j =0.

```
for ($k = 1; $k < $rows; $k++){
for ($j = 0; $j < $cols-1; $j++){
echo ($a[$k][$j]." ");
}
echo ("<br>");
}
```

The output of this is:

```
7 3
2 6
```

The maximum and minimum values of this matrix are 7 and 2 respectively.

Now, both rows and columns start at 1.

```
for ($k = 1; $k < $rows; $k++){
for ($j = 1; $j < $cols; $j++){
echo ($a[$k][$j]." ");
}
echo ("<br>");
}
```

The output of this is:

```
3 5
6 9
```

The maximum and minimum values of this matrix are 9 and 3 respectively.

__The Minimum and Maximum values Matrices__

To merging the minimum values to form other matrix of minimum values using arrays, use

```
#minimum value
echo "<br>";
$b =array(array(1,3),array(2,3));
$rows_b = count($b);
$cols_b = count($b[0]);
for ($i = 0; $i < $rows_b; $i++){
for ($l = 0; $l < $cols_b; $l++){
echo ($b[$i][$l]." ");
}
echo ("<br>");
}
```

This results to a matrix of the form

```
1 3
2 3
```

The same concept is applied to maximum values using

```
$c =array(array(7,7),array(7,9));
$rows_c = count($c);
$cols_c = count($c[0]);
for ($m = 0; $m < $rows_c; $m++){
for ($n = 0; $n < $cols_c; $n++){
echo ($c[$m][$n]." ");
}
echo ("<br>");
}
```

resulting in the 2x2 matrix below.

```
7 7
7 9
```

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