"数值分析大作业及Matlab程序：解线性方程组的直接法与误差分析"

Summary: The given assignment for a Numerical Analysis course involves solving linear systems of equations using direct methods, specifically the column principal Gaussian elimination method. The assignment includes three parts: adding a perturbation to the vector b, adding perturbations to the elements a22 and a66 of matrix A while keeping b constant, and conducting error analysis for the solutions of the perturbed systems. The mathematical principles involved in the assignment are outlined, and the direct method of column principal Gaussian elimination is explained. The method involves transforming the original system of equations into an equivalent upper triangular system through a series of row operations. The given matrix A and vector b are used to illustrate the process and the resulting systems are solved to analyze the effects of perturbations on the solutions. The assignment also includes a MATLAB program for implementing the solutions. Overall, the assignment tests the understanding and application of direct methods for solving linear systems of equations in numerical analysis.