Solution of 3 equations in 3 unknownsFind the value of c which makes it possible to solve: u + v + 2 w = 2 , 2 u + 3 v − w = 5 , 3 u + 4 v + w = c

Question

Solution of 3 equations in 3 unknownsFind the value of   c which makes it possible to solve:  u  +  v  +  2  w  =  2  ,  2  u  +  3  v  −  w  =  5  ,  3  u  +  4  v  +  w  =  c

Aaron Everett · Accepted Answer

Set up your augmented matrix in the usual way:      [                            1                          1                          2                          2                                      2                          3                          −          1                          5                                      3                          4                          1                          c                      ]      .Then row-reduce it; reducing the first column, for instance, yields                    (1)                              [                                                    1                                            1                                            2                                            2                                                                    0                                            1                                            −                5                                            1                                                                    0                                            1                                            −                5                                            c                −                6                                              ]                        .            Now you can either stop and think about the equations corresponding to the bottom two rows of   (  1  ), or finish the row-reduction and then think about what   c has to be to avoid having an inconsistent system.

Izabella Ponce · Accepted Answer

If you add the second and third equation you get   5  u  +  7  v  =  5  +  c ; if you multiply the second equation by   2 and then add it to the first then you get   4  u  +  u  +  6  v  +  v  =  12  =  5  u  +  7  v , so   c  =  7

Solution of 3 equations in 3 unknowns Find the value of c which makes it possible to solve:

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