MATRICES AND DETERMINANTS
Higher Concepts of Mathematics
Example: Find the determinant of A.
A =
6
2
1
3
Solution:
A
(6
3)
( 1 2)
18
( 2)
18
2
20
To expand a matrix larger than a 2 x 2 requires that it be simplified down to several 2 x 2
matrices, which can then be solved for their determinant. It is easiest to explain the process by
example.
Given the 3 x 3 matrix:
1
3
1
4
1
2
5
6
3
Any single row or column is picked. In this example, column one is selected. The matrix will
be expanded using the elements from the first column. Each of the elements in the selected
column will be multiplied by its minor starting with the first element in the column (1). A line
is then drawn through all the elements in the same row and column as 1. Since this is a 3 x 3
matrix, that leaves a minor or 2 x 2 determinant. This resulting 2 x 2 determinant is called the
minor of the element in the first row first column.
MA-05
Page 22
Rev. 0
