In this page matrix determinant we are going to see how to find determinant for any matrix and examples based on this topic.
Definition :
For every square matrix A of order n with entries as real or complex numbers, we can associate a number called determinant of matrix A
It is denoted by |A| or det (A) or ∆.
Example 1 :
Find determinant of the following matrix.
|
Solution :
A= |
|
= 3 |
|
-4 |
|
+1 |
|
= 3 [ -6-(-4) ] -4 [ 0-10 ]+1 [0-(-5)]
= 3 [ -6+4 ] -4 [ -10 ]+1 [5]
= 3 [ -2 ] -4 [ -10 ]+ 1 [5]
= -6 + 40 + 5
= -6 + 45
= 39
Example 2 :
Find determinant of the following matrix.
|
Solution :
= 1 |
|
-1 |
|
-1 |
|
= 1 [1-2 ] -1 [ 2-(-2) ] - 1 [-2-1]
= 1 [-1] -1 [ 2+2 ] - 1 [-3]
= -1 -1 (4) + 3
= -1 -4 + 3
= -5 + 3
= -2
Example 3 :
Find determinant of the following matrix.
|
Solution :
=1 |
|
-2 |
|
+3 |
|
= 1 [ -3 - 0 ] -2 [ 1 - 8 ] + 3 [0 - 6]
= 1 [ -3 ] -2 [ -7 ] + 3 [- 6]
= -3 + 14 - 18
= -21 + 14
= -7 matrix determinant matrix determinant matrix determinant
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