First see following example
1 2 3 । A । = 4 5 6 7 8 9
Above is determinant and we can calculate its value by expending it
If we calculate co-factors of first row and then multiply with respective element and then sum of these . After this what we found will be the value of determinant .
You should also know co-factor
What is co- factor ?
If we multiply - 1's power m + n with minor , then what we obtain will be co -factor .
You should also know minor
What is minor
Minor is submatrix , if we leave selected element's row and column
for example
------1 2 3 । A । = 4 5 6 7 8 9------------- 5 6 1's minor is = 8 9
1' co-factor = - 1's power ( 1+1 because it is first row and first column element ) and
multiply with 5 6
--------------- 8 9
Now , you will able to calculate the value of determinant
। A । = 1 X 5 6 - 2 X 4 6 + 3 X 4 5
8 9 7 9 7 8
। A । = 1 X ( 9 x 5 - 6 X 8 ) - 2 ( 9 X 4 - 7 X 6 ) + 3 X ( 8 X 4 - 7 X 5 )। A । = -3 + 12 -9 = 0
So , value of determinant is Zero
