Question 98
The numbers from the table
| $a_{11}$ | $a_{12}$ | $\cdots$ | $a_{1 n}$ |
| :---: | :---: | :---: | :---: |
| $a_{21}$ | $a_{22}$ | $\cdots$ | $a_{2 n}$ |
| $\vdots$ | $\vdots$ | | $\vdots$ |
| $a_{n 1}$ | $a_{n 2}$ | $\cdots$ | $a_{n n}$ |
satisfy the inequality
$$
\sum_{i=1}^{n}\left|a_{i 1} x_{1}+a_{i 2} x_{2}+\cdots+a_{i n} x_{n}\right| \leq M
$$
for every choice $x_{i}= \pm 1$. Prove that $\left|a_{11}\right|+\left|a_{22}\right|+\cdots+\left|a_{n n}\right| \leq M$.
| $a_{11}$ | $a_{12}$ | $\cdots$ | $a_{1 n}$ |
| :---: | :---: | :---: | :---: |
| $a_{21}$ | $a_{22}$ | $\cdots$ | $a_{2 n}$ |
| $\vdots$ | $\vdots$ | | $\vdots$ |
| $a_{n 1}$ | $a_{n 2}$ | $\cdots$ | $a_{n n}$ |
satisfy the inequality
$$
\sum_{i=1}^{n}\left|a_{i 1} x_{1}+a_{i 2} x_{2}+\cdots+a_{i n} x_{n}\right| \leq M
$$
for every choice $x_{i}= \pm 1$. Prove that $\left|a_{11}\right|+\left|a_{22}\right|+\cdots+\left|a_{n n}\right| \leq M$.