We have a matrix A for which we want to give an estimate of the condition number. We know that the system Ax = b with input b = (4, −8, 1)T has solution x = (2, 1, 0)T
We also know that a somewhat modified right-hand vector b˜ = (4, −8, 2)T solves the system A˜x = b˜, where ˜x = (8, 11, −3)T.