The order of a matrix encompasses both the number of rows and columns and expresses it by multiplying both.
In other words, the order of a matrix is the number of rows and the number of columns that a matrix has, regardless of whether they are different.
The order of the matrices and areas of the rectangles
The order of the matrices can be easily understood if we relate it to the formula for the area of the rectangle. We speak of a rectangle and not a square because the rectangle can become a square if its sides are equal, but not vice versa. Therefore, we will do the associative example by means of a rectangle.
The order of a matrix is also called dimension since it could be described as the units of the space that the matrix occupies.
If a matrix is square, we will see that the number of rows coincides with the number of columns and, therefore, the two numbers multiplied in the order will be equal and the matrix will have the shape of a square.
Given any rectangle, its area would be:
The area of the rectangle is calculated by multiplying the length of the segment to by segment length b. This length of the segment is expressed in unit terms, that is, if the segment to has a length of 3, we can also say that it has a length of three unit units.
In matrix terms, this length can be understood as the number of rows which has an array. To express the columns we can use the same logic above. The length of the segment b, expressed in unit units, can be understood as the number of columns that a matrix has. The above matrix would be a = 3 and b = 4.
Difference between order and area
The difference between finding the dimension or order of a matrix and calculating the area of a rectangle is that we will express the multiplication of the rows by the columns without calculating the result. In other words, in the area of the rectangle we would calculate the value of the multiplication, but when it comes to the order of a matrix, this multiplication is not calculated. This condition can be seen in the subscript that the matrix has:
Determine the order of the following matrices:
The descending ordered solutions would be: 3 × 4, 3 × 2, 2 × 5, 2 × 1.