2. 4 For $\{1,2,3, \cdots, n\}$ and each of its non-empty subsets, we define the "alternating sum" as follows: arrange the numbers in the subset in decreasing order, then alternately add and subtract the numbers starting from the largest (for example, the alternating sum of $\{1,2,4,6,9\}$ is $9-6+4-2+1=6$, and the alternating sum of $\{5\}$ is 5). For $n=7$, find the total of all these alternating sums.
[Solution] Obviously, the non-empty subsets of the set $\{1,2,3,4,5,6,7\}$ total $2^{7}-1=127$, and each element appears $2^{6}=64$ times in the subsets.

According to the problem, the numbers $1,2,3,4,5,6$ each appear 32 times in odd positions and 32 times in even positions in the subsets, so the alternating sum of these numbers in the subsets is 0. The number 7 also appears 64 times, and it always takes a positive value, so the total alternating sum of all subsets is
$$7 \times 64=448$$