For which real values of t does the following system of linear equations: { t x 1 + x 2 + x 3 = 1 x 1 + t x 2 + x 3 = 1 x 1 + x 2 + t x 3 = 1 Have:a) a unique solution?b) infinitely many solutions?c) no solutions?

Question

For which real values of t does the following system of linear equations:      {                            t                      x            1                    +                      x            2                    +                      x            3                    =          1                                                  x            1                    +          t                      x            2                    +                      x            3                    =          1                                                  x            1                    +                      x            2                    +          t                      x            3                    =          1                        Have:a) a unique solution?b) infinitely many solutions?c) no solutions?

Nathalie Rivers · Accepted Answer

You can write your system of equations in vector/matrix form:      [                            t                          1                          1                                      1                          t                          1                                      1                          1                          t                      ]        [                                        x            1                                                            x            2                                                            x            3                                ]    =      [                            1                                      1                                      1                      ]  This has now the form   A  x  =  b where   A is the matrix   x the unknown and   b the vector of ones. If it can be solved the solution would be   x  =      A          −      1        b. Now determining whether you can solve this by consulting the determinant of   A or the gaussian algorithm.

memLosycecyjz · Accepted Answer

1)   1)If     t  =  1   the system reduces to just one equation, and it has         ∞    2    solutions.2)   2)If      t  =  −  2   there are no solutions.3)   3)If     t  ≠  1  ,  −  2   there is a unique solution, depending on t.

For which real values of t does the following system of linear equations: {tx_1+x_2+x_3=1, x_1+tx_2+x_3=1, x_1+x_2+tx_3=1

Answered question

Answer & Explanation

New Questions in Algebra I