The linear system is called ill conditioned, if small changes in the coefficients of equations result in small changes in the values of the unknowns.

What is ill-conditioned problem?

In non-mathematical terms, an ill-conditioned problem is one where, for a small change in the inputs (the independent variables) there is a large change in the answer or dependent variable. This means that the correct solution/answer to the equation becomes hard to find.

When should a system be called an ill-conditioned system while solving equations?

The system of equations (6.20) is called ill-conditioned when the change in y is too large compared to the solution vector x of (6.20). Otherwise, the system of equations is called well-conditioned. If a system is ill-conditioned then the corresponding coefficient matrix is called an ill-conditioned matrix.