You can
put this solution on YOUR website! Calculate the co-factor of the element 2:
|1 2 3|
|3 4 5|
|5 6 7|
1. Create the 2×2 MINOR determinant of the element 2.
Make the 2×2 determinant by choosing the 4 elements which are NOT in the
same row and NOT in the same column with 2. That 2×2 MINOR determinant is
Minor of 2 = |3 5|
|5 7|
2. Give that minor determinant its correct sign:
Use this "checkerboard" sign-scheme 3x3 matrix to decide whether to assign
the minor determinant a + sign or a - sign:
|+ - +|
|- + -|
|+ - +|
We see that in the original determinant
|1 2 3|
|3 4 5|
|5 6 7|
the 2 in in the middle of the top row and we see that in the sign-scheme
determinant above, there is a - sign in the middle of the top row. Therefore
we give the minor determinant a negative sign, and the cofactor is
|3 5|
(-1) times the minor |5 7| = (-1)·(3·7 - 5·5) = -(21 - 25) = -(-4) = 4
So the cofactor of 2 in the original determinant is 4.
Edwin
