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Matrices

The Hook

The code of the Matrix.

What is it?

A rectangular array of numbers arranged in rows and columns.

Time Travel (History)

Developed by Cayley in 1858. The foundation of modern computer graphics.

Cheat Code

RC Cola: Multiply Rows by Columns.

Practice This Now!

The Field Guide

In Plain English: A matrix is a spreadsheet box of data. Instead of solving one equation, matrices let us solve whole systems at once. They are the engine behind 3D video games—spinning a character is just multiplying a matrix.

In The Real World: CGI Animation. Rotating, scaling, and moving 3D models uses 4x4 matrices.

How To Do It

  1. Check dimensions: You can only multiply if Inner Numbers match (2x3 and 3x4 works).
  2. Multiply Row 1 of First Matrix by Column 1 of Second Matrix.
  3. Add the products together.
  4. Repeat for every spot in the grid.
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Booby Trap!

Thinking A x B is the same as B x A. In matrices, order matters. You usually can't switch them.

Real World Challenge
"Store A sells 2 Apples, 3 Bananas. Store B sells 4 Apples, 1 Banana. Prices are $1 and $0.50. Use matrices to find revenue."
The Logic: [2 3; 4 1] times [1; 0.50]. Row 1: 2*1 + 3*0.5 = 3.5. Row 2: 4*1 + 1*0.5 = 4.5.

Training Drills

Notation
[ 1 2 ] [ 3 4 ]
2x2 Matrix.