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Matlab and Matrices

The Computing Engine

  Matlab is a calculator on Steroids

Has hundreds of built-in mathematical
functions that are built upon efficient

Some simple examples:

Numerically computes most calculus concepts
such as derivatives and integrals

Matrix operations such as numerically solving
complex systems of equations


Quick Intro to Variables


Like on your TI-83, you can assign variables to
remember answers, objects, and user input.

Example in Matlab:

x = 3;

Note: the semicolon suppresses the output on the command
line, try x = 3 without it and you will see!

Now you can use this variable x later in different
mathematical operations (if used in the command line
window, it is a global variable meaning it can be used
anywhere in Matlab)

Keep track of your variable names!!!!!

Let’s add some numbers…

2 + 2 on the command line

See the answer that comes out
(hopefully 4)

The ans variable

Stands for “answer”

Default variable for all common unassigned
operations done in command line window

See how it appears in the variable
workspace window?

Order of Operations


“Please Excuse My Dear Aunt Sally”

Parentheses, Exponent, Multiplication
Division, Addition, Subtraction

Try it out:

2 + 2 / 4 = 2.5

(2 + 2) / 4 = 1


Matlab and Matrices

The name Matlab

“Matrix Laboratory”

Originally an open application that came out
of the Argonne government research
institution (free!)

Initially designed for doing complex
algorithms involving matrices in linear
algebra and engineering applications

Matrices in Matlab

A foundational programming type

Representing it in Matlab:

A = [1 2 3; 2 0 2; 3 1 9]

Semi-colons mean new lines, spaces between numbers
represent row placement (you can also use commas)

More Matrices

Keep in mind that a matrix can be a
single row! Some call this a vector.

A 3 element row-vector ( a 1x3 matrix) is
easy to type out, but what if you need a
100 element row-vector?

Try the syntax:

t = 1:100 or

t = 1: 1: 100

What if you did “t = 1 : 0.01 : 100” ?

Matrix Operations

Multiply a 3 x 3 Matrix with another:

A x B


Built-in Matlab Functions

Determinant of our Matrix A


Inverse of our Matrix B



Built-in Matlab Functions

Some more basic operations:

sqrt(4) – takes a square root of a number

mod(4,3) – modulus (we will use this later)

reciprocal(5) – gives the reciprocal of a number

cos(t) – gives the cosine of variable t

Note: if t is a row-vector, Matlab is adept enough to
recognize that it should take the cosine of each element
in t, and returns a row vector that is same length of t

exp(4) – represents e4

log(4) – represents the natural log of 4 ( ln(4) )


Assign variables x, y, a, b for different
values of a sine function

Put these variables into a row-vector A

Plot A over a domain of 4 values

Get a good representative plot of a sine

Improve the “resolution” by specifying more
values for the independent variable