Goals for today Learn to create, combine, and index arrays Learn to multiply arrays in MATLAB Use matrix multiplication to simulate a real-world problem Thursday, June 30 th, 2016

Last time: assignment addition/subtraction multiplication/division exponentiation expression target = expression a + b a - b a*b a/b a^b a b result order of operations: PEMDAS () ^ * / + -

Vectors, matrices, and multi-dimensional arrays columns rows pages

Creating arrays A = [5, 2, 1; 3, 2, 7] separate elements on a row with a comma separate rows with a semicolon

Special commands for creating arrays eye(n) ones(n, m) zeros(n, m) start:step:end

Transpose arrays with the ‘ operator F = A’ AF G = B’ B G

Join arrays together with square brackets ABC A D E

Think-Pair-Share: Can these arrays be joined? (1) (2)(3)

Retrieving parts of an array: “indexing” A(1, 2) row(s) column(s)

Retrieving parts of an array: “indexing” A(2, 3)

Multiple indices A([1, 2, 3], [2, 3]) rows columns

Multiple indices A(:, [2, 3]) shorthand for “all rows”

practice… (a) (d) (f) (e) (c) (b)

Matrix multiplication

Visualizing matrix multiplication

3 rows 3 columns 3x3 matrix

Multiplying arrays

Will they multiply? N

Properties of Matrix Multiplication Yes or no?

Multiplying rabbits

Can you help the rabbits survive longer without becoming overpopulated? What happens to the population over time? What happens when you change the birth rate? What happens when you change the survival rates?