please help me with this question Consider the two systems of equations below. a

Question

please help me with this question Consider the two systems of equations below. a) Attempt to solve these systems using the programs GaussNaive & GaussPivot. Does the program give a solution for the system that does not have one? b) Look closely at the augmented matrices that are shown when the program is run. Write your observations-does this give you any insight on the meaning of linearly dependent equations? 6x_1 + 3x_2 + 9x_3 + 9x_4 = 48 8x_1 - 7x_2 + x_3 = - 62 Sys1: - 7x_1 - 4x_2 - 11x_3 + 6x_4 = 91 8x_1 + x_2 + 9x_3 - 6x_4 = - 107 6x_1 + 3x_2 + 9x_3 + 9x_4 = 48 8x_1 + 8x_2 + x_3 = - 62 Sys2: - 7x_1 - 4x_2 - 11x_3 + 6x_4 = 91 8x_1 + x_2 + 9x_3 - 6x_4 = - 107

Explanation / Answer

Proceeding in this way we find that System I has no solution.

System II has solution as

{ x1 = -9, x2 = 1, x3 = 2, x4 = 9 }.

System I is linearly dependent and hence have no unique solution but dependent solutions.

System I System 2 Augmented matrix 6 3 9 9 48 6 3 9 9 48 8 -7 1 0 62 8 8 1 0 -62 -7 -4 -11 6 91 -7 -4 -11 6 91 8 1 9 -6 -107 8 1 9 -6 -107 -1 -1 -2 15 139 -1 -1 -2 15 139 0 -8 -8 6 169 0 7 -8 6 45 0 3 3 -99 -882 0 3 3 -99 -882 0 -7 -7 114 1005 0 -7 -7 114 1005

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