Assignment 22

"One cannot escape the feeling that mathematical formula have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even then their discoverers, and that we get more out of them than was originally put into them." -- (Heinrich Hertz)

Math History Tidbit:

Some 1500 years ago, an American Indian people called the Anasizi lived in what is now the southwestern United States. They, along with the Navajo and Pueblo tribes, produced coiled baskets, rugs, quilts, and clothing that displayed complex geometric patterns.

Blankets produced by Native Americans had what is sometimes called line symmetry, turn symmetry, and rotational symmetry. People long ago used mathematical thinking to produce some amazing designs. Some of these blankets and rugs, of called the "first American tapestries," are now in museums for everyone to admire.


Herkimer's Corner

How did Herkimer discover that it was raining cats and dogs?

Answer: When he went outside, he stepped into a poodle.

Herky 's friends:

LUKE WARM...this guy doesn't like things too hot.

ISSIAH LOTT...nobody can get this fellow to shut up.


Reading: Section 4.1, pages 199-202.

Exercises: Pages 203-204/29-36, 43,44

Items for reflection:

Mathematical word analysis:
MATRIX: From the Latin word matrix (pregnant animal). A modern dictionary provides this definition: "That which gives form, origin, or foundation to something enclosed or embedded in it." In a manner of speaking, a matrix is an array of numbers that has embedded in it the potential for use in problem solving.

A matrix is a rectangular array of numbers in rows and columns. They can be very useful in data representation, and for representing equations that need to be solved. While it is not an objective of this assignment, you will eventually learn that your calculator can make use of matrices to solve systems of equations.

Under certain conditions, matrices can be added, subtracted, and multiplied. In other words, you can apply number operations to matrices. These operations, of course, have to be clearly defined.

Note the MATRIX is a button on your TI-83 graphics calculator. We will learn how to do some basic calculator operations with matrices. In the TI-83 Graphing Calculator Guidebook, you can read about matrix operations beginning in section 10.1.

Due to the limitations of available symbolism here, the demonstrations below will be with matrices having just one row.

Problem: If A = [2 5 1 3] and B = [-1 2 4 2], calculate

(a) A + B
(b) A - B
(c) 4A + 3B

Solution (with communication):

(a) [2 5 1 3] + [-1 2 4 2] = [1 7 5 5]

(b) [2 5 1 3] - [-1 2 4 2] = [3 3 -3 1]

(c) 4[2 5 1 3] + 3[-1 2 4 2] = [8 20 4 12] + [-3 6 12 6] = [5 26 16 18]