Combining Information

Linear Algebra (Matrices) · Axiom Academy

Two stores, three products, a price list — watch matrix multiplication fold a table of quantities into a table of dollars. You run a small chain with a Downtown and an Uptown store, each stocking phones, laptops, and watches — and you want this week's revenue per store . You have two tables; multiplying them combines them. Two tables, waiting to be combined One table holds how many of each item each store has. The other holds what each item is worth . Nudge a price and watch — these are the two inputs matrix multiplication is about to fuse. One row meets the price column Here's the whole trick: slide a store's row of quantities along the column of prices, multiply each pair, and add. That running sum IS that store's revenue — a row times a column. Combine the whole table at once Do that row-times-column for every store and you get a revenue figure for each. Add a second price column — a weekend sale list — and the answer grows into a full table: store by pricing scenario. Matrix multiplication is just combining tables : each output cell is one row dotted with one column — multiply the matching pieces, add them up. Wherever a quantities table meets a rates table — units × price = revenue, ingredients × cost = cost-per-dish, hours × wage = payroll — this same row-times-column move does the combining.

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.