Question

Solve, in D3 , the system with the same r.h.s. annd with b=(01). Verify that, in this case, the residual is higher while the solution is actually much more accurate. This shows you that not necessarily the "worst case scenario" takes place and remind you that the residual is not necessarily a measure of how accurate is a solution of a linear system

Answer 1

To solve the system in D3 with the same right-hand side and with b=(0 1), we can use an analytical technique such as Gaussian elimination. By performing row operations on the augmented matrix, we can reduce it to row-echelon form and then to reduced row-echelon form, which will give us the solution.

Step-by-step explanation:

To solve the system in D3 with the same right-hand side and with b=(0 1), we can use an analytical technique such as Gaussian elimination. By performing row operations on the augmented matrix, we can reduce it to row-echelon form and then to reduced row-echelon form, which will give us the solution. By comparing the residuals of this solution with the residuals of the graphical solution, we can see that the analytical technique is potentially more accurate.

The analytical technique involves precise calculations and eliminates any approximation errors. On the other hand, the graphical technique relies on reading values from a graph, which may have limitations due to the accuracy of the graph itself. Therefore, the analytical technique provides a more precise and accurate solution.