In this question, the solution of a set of linear algebraic equations using Point$-$Jacobi and Gauss$-$Seidel iterative approaches will be considered. Please refer to the codes provided in the module on CANVAS.

Providing evidence of your approach in a spreadsheet or word document, carry out Point$-$Jacobi and Gauss$-$Seidel iterative approaches on the following set of equations:

$-3x_1+1x_2+10x_3+1x_4-2x_5=5$

$2x_1+1x_2-1x_3-2x_4+11x_5=32$

$2x_1+11x_2+1x_3-3x_4+1x_5=17$

$1x_1-2x_2+1x_3+14x_4+3x_5=55$

$8x_1+2x_2-1x_3+1x_4-1x_5=23$

Complete the following:

Providing screenshots and commentary, carry out an investigation using both the Point$-$Jacobi and Gauss$-$Seidel iterative approaches using the given MATLAB code. Consider different tolerances $($i$.$e$.,$ Tol $=0\mathrm{.}1,0\mathrm{.}01$ and $0\mathrm{.}001.$ What are the implications of the variations in these values of tolerance? What is the error associated with each answer for the values of $x_1,x_2,x_3,x_4,$ and $x_5$ for these variations in tolerance? Comment on the number of iterations required to achieve convergence in each instance. What conclusions can be drawn from this investigation?

including

evidence of the following:

Any code used

Results $[60\%$ of each question$]$ Statement and, where appropriate, justification of input parameters or manipulation of the provided information. Evidence, where approprizte, of verification of the results should be $p\text{'}$ ovided.

Discussion and Conclusions $($State tre advantages and disadvantages of each approach;