Finding the amount of solutions in a 3 equation solution x + 2 y + 3 z = 7 3 x + 4 y − z = 4 3 x + 2 y − 11 z = − 13

Question

Finding the amount of solutions in a 3 equation solution  x  +  2  y  +  3  z  =  7  3  x  +  4  y  −  z  =  4  3  x  +  2  y  −  11  z  =  −  13

Elianna Douglas · Accepted Answer

We have the system  x  +  2  y  +  3  z  =  7  3  x  +  4  y  −  z  =  4  3  x  +  2  y  −  11  z  =  −  13The associated augmented coefficient matrix is given by:      (                            1                          2                          3                                  |                          7                                      3                          4                          −          1                                  |                          4                                      3                          2                          −          11                                  |                          −          13                      )  Use Gaussian Elimination (row reduction using elementary row operations). If you encounter a row with all zeros, then you&#039;ll know there are infinitely many solutions. You&#039;ll have an inconsistent system, for which there are NO solutions, if you obtain a row such as  (  0    0    0    |    a  )where   a  ≠  0. Otherwise, the system will have one unique solution.If you row reduce correctly, you should obtain a reduced row form as follows:      (                            1                          0                          −          7                                  |                          −          10                                      0                          1                          5                                  |                                      17            2                                                0                          0                          0                                  |                          0                      )

flightwingsd2 · Accepted Answer

[                            1                          2                          3                          7                                      3                          4                          −          1                          4                                      3                          2                          −          11                          −          13                      ]        [                            1                          2                          3                          7                                      0                          −          2                          −          10                          −          17                                      0                          −          4                          −          20                          −          34                      ]        [                            1                          2                          3                          7                                      0                          −          2                          −          10                          −          17                                      0                          0                          0                          0                      ]    0  =  0Infinite amount of solutions

Finding the amount of solutions in a 3 equation solution x + 2 y + 3 z = 7

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