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

besnuffelfo 2022-09-23 Answered
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?
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Answers (2)

Nathalie Rivers
Answered 2022-09-24 Author has 7 answers
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.
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memLosycecyjz
Answered 2022-09-25 Author has 2 answers
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. 
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