Determinants
2 x 2 and 3 x 3 Matrices
Note that Matrix is the
singular form, matrices is
the plural form!
Matrices
A matrix is an array of
numbers that are
arranged in rows and
columns.
A matrix is “square” if
it has the same
number of rows as
columns.
We will consider only
2x2 and 3x3 square
matrices
1
3
-½
0
-3
8
¼
2
0
-¾
4
180
11
Note the difference in the
matrix and the
determinant of the matrix!
Determinants
Every square matrix
has a determinant.
The determinant of a
matrix is a number.
We will consider the
determinants only of
2x2 and 3x3 matrices.
1
3
-½
0
-3
8
¼
2
0
-¾
4
180
11
Determinant of a 2x2 matrix
1
3

 1 0   3  1
-½
0
2   3 2
Determinant of a 3x3 matrix
Imagine crossing out the first row.
And the first column.
-3
8
¼
2
0
-¾
4
180
11
Now take the double-crossed element. . .
And multiply it by the determinant of the
remaining 2x2 matrix


 3  0 11
  3
4 180 
Determinant of a 3x3 matrix
•Now take the negative of the doublecrossed element.
•And multiply it by the determinant of the
remaining 2x2 matrix.
•Add it to the previous result.
Now keep the first row crossed.
Cross out the second column.
-3
8
¼
2
0
-¾
4
180
11


 3  0 11   3
4 180  8  211    3 4   4 
Determinant of a 3x3 matrix
Finally, cross out first
row and last column.
•Now take the double-crossed element.
•Multiply it by the determinant of the
remaining 2x2 matrix.
•Then add it to the previous piece.
-3
8
¼
2
0
-¾
4
180
11
 4  180  8  211    3 4   4 

  1    2 180    0  4    695
4
 3  0 11   3