The Gauss-Jordan Method of Finding the Inverse
In order to find the inverse of matrices larger that 2x2, we need a better method. If A is invertible and of size n×n, then we can find the matrix by the following method:
- Set up a matrix [A|I], a n×2n matrix where the left half is A and the right half is the identity matrix size n.
- Perform elementary row operations to reduce the left side to the identity matrix, while also performing those same operations on the right side.
- If A is invertible, when the left side is reduced to the identity matrix, the right side will be A-1. If the left side cannot be reduced to I, then A is not invertible.
Let's see an example of this below:
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