How do you find the inverse of #A=##((2, 4, 1),(-1, 1, -1), (1, 4, 0))#?
The inverted matrix is:
There are many ways in invert matrices, but for this problem I used the cofactor transpose method.
If we imagine that
Then we can define reciprocal vectors:
Each is easily calculated using the determinant rule for cross products:
We can use these to construct the cofactor transpose of
The reciprocal vectors and the cofactor transpose matrix have two interesting properties:
So we can determine that:
This means that: