system of linear equations: { ( 1 + b ) x + y + z = 1 x + ( 1 + b ) y + z = b x + y + ( 1 + b ) z = b 2 And I would like to know if it has zero, one, or more solutions depanding on b ( b ∈ R).How do I do that?

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system of linear equations:      {                            (          1          +          b          )          x          +          y          +          z          =          1                                      x          +          (          1          +          b          )          y          +          z          =          b                                      x          +          y          +          (          1          +          b          )          z          =                      b            2                                  And I would like to know if it has zero, one, or more solutions depanding on   b (  b  ∈  R).How do I do that?

sepolturamo · Accepted Answer

Hint: write down the augumented matrix and apply Gaussian elimination to it.Added: Here is what you should get      [                            1          +          b                          1                          1                          1                                      0                                                            b                              (                2                +                b                )                                                    1              +              b                                                                    b                          1              +              b                                                                                  b              +                                            b                              2                            −              1                                      1              +              b                                                            0                          0                                                                            (                b                +                3                )                            b                                      2              +              b                                                                                                                b                              3                            +              2                                                          b                              2                            −              b              −              1                                      2              +              b                                            ]    .Now, you should analyse the last row.

Monserrat Sawyer · Accepted Answer

suppose that   b  =  0 then you get  x  +  y  +  z  =  1  x  +  y  +  z  =  0  x  +  y  +  z  =  0clearly it has not solution,of course you can choose different b and test it,or try to reudce it to row echelon form and determine how given system is consistent or has solution.

system of linear equations: { <mtable columnalign="left left" rowspacing=".2em" columns

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