3 lines 4 variables linear equation gaussian { x + 2 y − z + 3 t = 3 2 x + 4 y + 4 z + 3 t = 9 3 x + 6 y − z + 8 t = 10

Question

3 lines 4 variables linear equation gaussian      {                                                                                    x                +                2                y                −                z                +                3                t                =                3                                                                                  2                x                +                4                y                +                4                z                +                3                t                =                9                                                                                  3                x                +                6                y                −                z                +                8                t                =                10

Brennan Frye · Accepted Answer

[                            1                          2                          −          1                          3                          3                                      2                          4                          4                          3                          9                                      3                          6                          −          1                          8                          10                      ]        [                            1                          2                          −          1                          3                          3                                      0                          0                          6                          −          3                          3                                      0                          0                          2                          −          1                          1                      ]        [                            1                          2                          −          1                          3                          3                                      0                          0                          2                          −          1                          1                                      0                          0                          0                          0                          0                      ]        [                            1                          2                          0                          2.5                          3.5                                      0                          0                          2                          −          1                          1                                      0                          0                          0                          0                          0                      ]    x  +  2  y  +  2.5  t  =  3.5    2  z  −  t  =  1you have infinitely many solutions

lurtzslikgtgjd · Accepted Answer

Put your system into the corresponding augmented matrix:  [  A  ∣  b  ]  =      [                            1                          2                          −          1                          3                          ∣                          3                                      2                          4                          4                          3                          ∣                          9                                      3                          6                          −          1                          8                          ∣                          10                      ]  then do Gaussian elimination. That is, row reduce to the RREF form. Then you can read off the solutions (if they exist). A solution will exists if and only if the rank of   A equals the rank of   [  A  ∣  b  ].

3 lines 4 variables linear equation gaussian { <mtable columnalign="left left" rowsp

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