Assess learners' ability to analyze conditioning and sensitivity of linear systems by computing and interpreting matrix and problem condition numbers (normwise and componentwise), deriving and applying perturbation bounds for Ax = b under coefficient and right-hand-side changes, relating forward and backward error, and evaluating algorithmic stability (e.g., Gaussian elimination, LU, QR) with numerical examples and interpretation of when solutions are stable, ill-conditioned, or require regularization.