Augment the matrix with the identity matrix with the
same dimensions (4×4):
We will use row operations until we get the identity on the left.
Multiply row 1 by -1 and add it to row 2:
Multiply row 1 by -1 and add it to row 3:
Multiply row 1 by -1 and add it to row 4:
Multiply row 2 by -1 and add it to row 1:
Multiply row 2 by 2 and add it to row 3:
Multiply row 2 by -2 and add it to row 4:
Add row 3 to row 1:
Multiply row 3 by 2 and add to row 4:
To avoid fractions multiply row 3 by -2 and row 2 by 3:
Add row 3 to row 2:
Again to avoid fractions multiply row 4 by 2 and row 1 by -3:
Add row 4 to row 1:
To avoid fractions multiply row 2 by 6:
Add row 4 to row 2:
To avoid fractions multiply row 4 by 2 and row 3 by 3:
Add row 4 to row 3:
Now get 1's on the diagonal:
Divide row 1 by -3
Divide row 2 by 18
Divide row 3 by 18
Divide row 4 by 12
Now that we have the identity on the left, the
augmented part is the inverse:
Edwin
