Could you help me please and give some tips on how should I prove it (show it).
Prove that Sol(A,b) of quadratic system of linear equations with n×n-Matrix:
$A =\begin{pmatrix} 1 & -1 & 0 & 0 & .. & 0& 0\\ 1 & 1 & -1 & 0& .. & 0 & 0\\ 0 & 1 & 1 & -1 & ..& 0& 0\\ .. & .. & .. & .. & .. & .. &..\\ 0 & 0 & 0 & 0 & .. & 1 & -1\\ 0 & 0& 0& 0& .. & 1 & 1 \end{pmatrix}$
for $n\geq 1$ and all b from $\mathbb{R}^{n}$ has only ONE solution.
Thank you in advance.