Determine whether the following system has a unique solution,no solution, or ind

Question

Determine whether the following system has a unique solution,no solution, or indefinitely many solutions. If a solution exists,write it down x1 +2x3 - X4 =5         2x1+ x2 + 3x3 =7         5x1+x2+9x3-3x4= 12

I am unsure of how to get started on this...do I use teh EchelonMethod or would I used the Gauss Jordan method?
Determine whether the following system has a unique solution,no solution, or indefinitely many solutions. If a solution exists,write it down x1 +2x3 - X4 =5         2x1+ x2 + 3x3 =7         5x1+x2+9x3-3x4= 12

I am unsure of how to get started on this...do I use teh EchelonMethod or would I used the Gauss Jordan method?

Explanation / Answer

A homogeneous system of linear equations has an infinite number of solutions if there are more unknowns than equations.  According to what is shown above, this system has 3 equations and 4 unknowns. This is fundamental theorem of Linear Algebra. Keep plugging away at it.

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