Find the solution set of triplets ( x , y , z ) that fulfil this system using Gauss-Jordan: { − x + 2 z = 0 3 x − 6 z = 0 2 x − 4 z = 0 First of all, I don't see any y variable there. I suppose it doesn't matter and I proceed normally: [ − 1 2 0 3 − 6 0 2 − 4 0 ] − f 1 [ 1 − 2 0 3 − 6 0 2 − 4 0 ] − 3 f 1 + f 2 [ 1 − 2 0 0 0 0 2 − 4 0 ] − 2 f 1 + f 3 [ 1 − 2 0 0 0 0 0 0 0 ] So, this is the staggered reduced form.This is an homogeneous system (because of the null column), thus one solution is ( 0 , 0 , 0 ).Other than that, I have to check out the range of the system. The range is 1, which is less than the number of columns... what is the number of columns?

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Find the solution set of triplets   (  x  ,  y  ,  z  ) that fulfil this system using Gauss-Jordan:      {                            −          x          +          2          z          =          0                                      3          x          −          6          z          =          0                                      2          x          −          4          z          =          0                        First of all, I don&#039;t see any   y variable there. I suppose it doesn&#039;t matter and I proceed normally:      [                            −          1                          2                          0                                      3                          −          6                          0                                      2                          −          4                          0                      ]    −      f    1        [                            1                          −          2                          0                                      3                          −          6                          0                                      2                          −          4                          0                      ]    −  3      f    1    +      f    2        [                            1                          −          2                          0                                      0                          0                          0                                      2                          −          4                          0                      ]    −  2      f    1    +      f    3        [                            1                          −          2                          0                                      0                          0                          0                                      0                          0                          0                      ]  So, this is the staggered reduced form.This is an homogeneous system (because of the null column), thus one solution is   (  0  ,  0  ,  0  ).Other than that, I have to check out the range of the system. The range is   1, which is less than the number of columns... what is the number of columns?

humusen6p · Accepted Answer

You are almost at the end.The number of parameters is   3  −  1  =  2, so we have two parameter say   y  =  t  ,  z  =  s and hence   x  =  2  s so the set of solutions are of the form  (  x  ,  y  ,  z  )  =  (  2  s  ,  t  ,  s  )  =  (  0  ,  0  ,  0  )  +  s  (  2  ,  0  ,  1  )  +  t  (  0  ,  1  ,  0  )which is a plane or 2 dimensional subspace

polivijuye · Accepted Answer

You have two variables. and three equations. Solve for   x and   z using any two, get   0  ,  0. Confirm that it is consistent with your third.Now deduce that all triples   (  x  ,  y  ,  z  )  =  (  0  ,  a  ,  0  ) where   a  ∈  R satisfy this, because your equations don&#039;t depend on   y.

Find the solution set of triplets ( x , y , z ) that fulfil...

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