85. Matrix Inverse
Where is the identity matrix (like the number in regular multiplication)
- For scalars:
- For matrices:
A matrix is invertible (nonsingluar) if:
- It is square ()
85.1. Calculating inverse
Row Reduction (Gauss-Jordan Elimination)
Augment with the identity matrix , and perform row operations until the left side becomes . The right side will then be
Example
Step 1. Set up augmented matrix
Step 2. Make the pivot of the first column equal to 1
Step 3: Eliminate the first column in row 2
Step 4: Make the pivot in row 2 a 1
Step 5: Eliminate the 0.5 above the pivot
So the inverse is: