For what values of the parameter t does the following system of equations have1. no solution2. more than one solution3. exactly one solutionFirst of all I wrote that as an augmented coefficient matrix: A = ( 1 1 t | − 1 3 ( t + 1 ) ( t − 1 ) | − 1 t 2 1 | 0 ) I suppose there'd be no solution if one of the lines showed inequality and exactly one if the rank of A is equal to the number of unknowns, but I don't know how to apply this here. Furthermore: what's the requirement for this system to have more than one solution?

Question

For what values of the parameter t does the following system of equations have1. no solution2. more than one solution3. exactly one solutionFirst of all I wrote that as an augmented coefficient matrix:  A  =      (                            1                          1                          t                                  |                          −          1                                      3                          (          t          +          1          )                          (          t          −          1          )                                  |                          −          1                                      t                          2                          1                                  |                          0                      )  I suppose there&#039;d be no solution if one of the lines showed inequality and exactly one if the rank of A is equal to the number of unknowns, but I don&#039;t know how to apply this here. Furthermore: what&#039;s the requirement for this system to have more than one solution?

HTMW7C0a · Accepted Answer

If the   det      A    0    ≠  0 (  rank  ⁡      A    0    =  3), then the solution exists and is unique.This gives you a cubic equation on   t, whose solutions have to be investigated individually.For each such   t, the solution exists (and is not unique) if   rank  ⁡  A  =  rank  ⁡      A    0   and there are no solutions otherwise.

Brooke Ayala · Accepted Answer

I had a problem with this question, thanks for the solution!

For what values of the parameter t does the following system of equations have 1. no solution 2.

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