Given the system of equations (123456789)(xyz)=(111)\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}147258369xyz=111, what is the nature of the solution set?
Unique solution
Infinitely many solutions
No solution
Only the trivial solution