Linear algebra: cofactors, signed minors
The tutor defines cofactor (aka signed minor) with an example.
In my post from Nov 24, 2014 I tell how to evaluate a determinant by hand.
Example: Evaluate the determinant of matrix A:
1 | 0 | -7 |
0 | 2 | 1 |
3 | 1 | 0 |
If the determinant is calculated from the top row, as follows
1[(-1)1+1(2×0-1×1)]+0[(-1)1+2(0x0-3×1)]+-7[(-1)1+3(0x1-3×2)]
we get
1[-1] + 0[3] -7[-6]
The numbers in red are called the cofactors or signed minors.
Cofactor Cmn is calculated as follows:
- Remove row m and column n.
- Calculate the determinant of the resultant matrix.
- Multiply that number by (-1)m+n
For every term in the matrix there is a signed minor.
I’ll be talking more about this:)
Source:
Johnson/Reiss/Arnold. Introduction to Linear Algebra. Don Mills: Addison-Wesley, 1989.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.
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