Assignment 23

"Every new body of discovery is mathematical in form, because there is no other guidance we can have." -- (Charles Darwin)

Math History Tidbit:

Persian-born Omar Khayyam (1048-1131) was both a poet and a mathematician. He is the author of a collection of poetry titled Rubaiyat. He contributed much to mathematics, including finding geometrical solutions for cubic equations and calendar reform, suggesting a cycle of 33 years that included 8 years with 366 days. Ever the poet, his reforms are referenced in the Rubaiyat:

Ah, but my Computations, People say,
Reduced the Year to better reckoning? -
'Twas only striking from the Calendar
Unborn Tomorrow, and dead Yesterday.

Khayyam's contributions to mathematics included discovering a geometrical solution for cubic equations. He was the first to be able to solve every type of cubic equation that possesses a positive root.

Herkimer's Corner

Why was Herkimer always tired on April 1?

Answer: He had just finished a March of 31 days.

Things Herky would like to know:

Why do you drive on a parkway and park in a driveway?

If a tree falls in a forest and no one is around to see it, do the other trees make fun of it?


Reading: Section 4.2, pages 208-210.

Exercises: Pages 211-213/17,18,19,23,33,34,37,38.

Items for reflection:

Mathematical word analysis:
ANGLE: From the Latin word angulus (a sharp bend). If you "bend" a line around a point, making two rays, you have an angle.

As this section indicates, matrices can be multiplied under certain conditions. You can multiply any two real numbers, but you can't necessarily multiply two randomly selected matrices.

Things to note:

If A and B are matrices, then the product AxB can be computed only if the number of rows in A is equal to the number of rows in B. If this is not the case, then the product AxB is not defined.

Also, matrix multiplication is not commutative. That is, the product AxB is generally not equal to the product BxA. In fact, it is quite possible that AxB may be defined, but BxA is not.

You can perform matrix multiplication on your TI-83 graphics calculator.


Problem: Explain how to use the TI-83 calculator to multiply the 2x2 matrices A and B, where

[4 2] = A

[3 5] = B
[2 9]

Solution (with communication):

Here is an outline of the calculator process:

MATRIX ---> EDIT ---> 1:[A]

MATRIX [A] 2 x 2
[4 2]
[1 8]

MATRIX ---> EDIT ---> 2:[B]

MATRIX [B] 2 x 2
[3 5]
[2 9]

QUIT (2nd, then MODE)... gets you out of EDIT mode.

MATRIX ---> 1:[A] ---> * ---> MATRIX ---> 2: [B] ---> ENTER

The calculator will display
[[16 38]
[19 77]]

The product of the two 2x2 matrices is the 2x2 matrix with 16 and 38 in the first row, and 19 and 77 in the second row.