We have the matrix $M_1=\begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 2\end{pmatrix}$ and its condition numbers are $\text{cond}_1=\|M_1\|_1\|M_1^{-1}\|_1=4\cdot 2=8$ and $\text{cond}_\infty=\|M_1\|_\infty\|M_1^{-1}\|_\infty=4\cdot 2=8$ .
We also have the matrix $M_2=\begin{pmatrix}2 & 1 & 0 \\ 2 & 2 & 1 \\ 0 & 1 & 2\end{pmatrix}$ and its condition numbers are $\text{cond}_1=\|M_2\|_1\|M_2^{-1}\|_1=4\cdot \frac{9}{2}=18$ and $\text{cond}_\infty=\|M_2\|_\infty\|M_2^{-1}\|_\infty=5\cdot 5=25$ .
We have to compare these conditions numbers to each other.
What exactly do we have to say?
At the first example we get the same condition number for both norms because the matrix is symmetrix, but at the second matrix we get different numbers since the matrix si not symmetric.
Is this the comparison that we have to say? Or what exactly do we have to compare?