Assess the learner's ability to analyze condition numbers and numerical stability when solving linear systems. Scope includes matrix conditioning and its interpretation, computing and comparing matrix and problem condition numbers, impacts of floating-point rounding and pivoting on LU factorization, stability of QR factorization, convergence and stability considerations for iterative methods (Jacobi, Gauss–Seidel, Conjugate Gradient), and use of forward/backward error and residuals to evaluate solver accuracy; expect qualitative comparisons and brief computational interpretation for selecting appropriate solvers.