In each part,determine whether the given vector is a solution of the linear system
\begin{align} 2x-4y-z&=1\\ x-3y+z&=1\\ 3x-5y-3z&=1 \end{align}
(a) $(3,1,1)$ (b) $(3,-1,1)$ (c) $(13,5,2)$ (d) $(13/2,5/2,2)$ (e) $(17,7,5)$
It's easy to solve this question. Just plug in the given vector into 3 equations respectively and check that if the left and side = the right hand side. And it turns out that a.d.e meet the restrictions of all 3 equations.
But my question is: why is that possible? Since for a linear system with n equations and n unknowns, it has only 1 unique solution. Geometrically, this linear system is like 3 planes, and the solution is a point when these 3 planes coincide. So, I think there's only 1 point that can suit into this linear system.