What is a matrix and how do we use grids of numbers?

Imagine you walk into a parking garage and every spot is labeled by row and column. Spot in row 3, column 5. That neat arrangement of slots — rows going across, columns going down — is the whole secret behind a matrix. A matrix is just a grid of numbers parked in tidy rows and columns. Nothing scarier than that.
So why bother lining numbers up in a grid? Because a grid keeps each number's MEANING in its position. Picture a tic-tac-toe board where every square holds a number instead of an X or O. The top-left number means one thing, the bottom-right means another, just because of where they sit. The grid is a little filing cabinet — the spot tells you what the number is FOR.
