Inflight Conundrums

Here are two puzzles taken from an inflight magazine.

Puzzle 1

Which symbol should replace the ?

First, express this table of symbols as a matrix.

Then, introduce the unknowns and to represent the sum of the second and third rows respectively, so as to obtain equations for each row.

Similarly, introduce and for the sum of the third and fourth columns respectively.

Together, these equations allow us to determine all the unknowns.

To determine which symbol should replace the , we use pattern-matching.

Hence should replace .

Puzzle 2

What is the value of the column with total ?

The solution is immediate.

Indeed, you can solve for all symbols if you want.