Let $A\in\mathbb R^{m×m}$ with $a_{11}=2$, $a_{12}=-1$, $a_{m,m-1}=-1$, $a_{mm}=2$ and for $2\leq i\leq m-1$: $a_{ii}=\dfrac52$,$$a_{ij}=\begin{cases}−\dfrac43,&\text{if }|i−j|=1\\\dfrac1{12},&\text{if }|i−j|=2\end{cases}$$
For instance, for $m = 6$: $$A = \begin{bmatrix} 2& -1& 0& 0& 0& 0\\ −\frac{4}{3}& \frac{5}{2}& −\frac{4}{3}& \frac{1}{12}& 0& 0\\ \frac{1}{12}& −\frac{4}{3}& \frac{5}{2}& −\frac{4}{3}& \frac{1}{12}& 0\\ 0& \frac{1}{12}& −\frac{4}{3}& \frac{5}{2}& −\frac{4}{3}& \frac{1}{12}\\ 0& 0& \frac{1}{12}& −\frac{4}{3}& \frac{5}{2}& −\frac{4}{3}\\ 0& 0& 0& 0& -1& 2 \end{bmatrix} $$
Why the condition matrix of this matrix is large? Is there an intuitive way to determine that without calculating?