Yes. Ill conditioned matrices are hard to “invert” (more like solve Ax=b for a given A and b) almost by definition. The condition number is basically a measur

Yes. Ill conditioned matrices are hard to “invert” (more like solve Ax=b for a given A and b) almost by definition. The condition number is basically a measure if sensitivity. If I change b a little, the change in x is proportional to b multiplied by the condition number. If the matrix is very ill conditioned (say more than 1e10 for a double precision algorithm), the matrix is really singular for any practical purpose, so the problem is really ill posed.