Consider a matrix of coefficients, a vector of unknowns and a vector of solutions satisfying
You're given that there exists a left inverse of satisfying
Consider the following argument
- Multiplying both sides with on the left,
- Hence, satisfies
- Substituting back in ,
- Hence, is a right inverse of .
But that was not what we were originally given. Which is the first statement that went wrong?
Inspired by Artin's Algebra