#overexplanation

A matrix is one way to represent a system of numbers, be they coefficients of a system of equations (most common/useful), or values in a table, or whatever else.

They're useful because you can manipulate values in matrices into interesting forms (like row-eschelon and diagonal and lower diagonal and such) that can help you find answers to systems much easier than working with all the information at once.

For example, if I wanted to find the solution set to a system of equations like

a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = b_1

a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = b_2

a_{31}x_1 + a_{32}x_2 + a_{33}x_3 = b_2

Then I could turn it into the system Ax = b, where A is a matrix, x and b are vectors (basically n by 1 matrices or a single vertical column of numbers), and A and b are given. Doing this would allow me to manipulate the coefficients, which are what go into A, using row operations (which I can describe in a second), so that it's easier to use the values of the b vector to find the values of the x vector.

(hence the username)

(also i just love the adjective sly)

(like, its definition as well)

Hmm, maybe I'm really NOT as funny as I thought. :S

Hint 1: The joke works best if you say it aloud.

Hint 2: A urine sample (or other body fluid samples) are often referred to as "specimen" for lab testing.

Hint 3: Try pronouncing "space-man" in a really bad Italian accent.