-1/2

-1/121

Application Activity 2:

bor

1/4

14]

0

-5/24

23

1/6

[18]

Encoding/decoding Messages

Did you obtain the original message?

O

1. Choose a message that you want to encode. It should have between 20 and 30 letters.

6. Explain the process of encoding and decoding messages by using linear algebra.

Assign a number to every letter according to the order the letter has in the American

7. Do you know any other methods to encode and decode messages using mathematics?

alphabet. For example, A=1, B=2, C=3, etc. Use 27 to denote a space.

Describe one method in detail. You can use the internet to answer this question.

2. Choose an invertible 3x3 matrix. Show that the matrix is invertible.

Rubric

3. Divide your message into 3-letter groups. If the last group does not have enough letters,

use 27 for the remaining spaces. Encode each group of your message by left multiplying

In addition to the assigned points, your writing must follow proper rules of grammar and

the matrix by the group. You may use a TI-84 calculator to perform the computations.

mechanics of writing. It must also comply with APA requirements especially referencing

and citation.

You must show your work and explanation in detail to receive full credit. Just an answer

For example, if the matrix is

without any explanation is worth 0 points. To err on the side of caution here, if unsure,

please touch base with your instructor.

Question

Total Points Possible

Comments

and the message is ABC, A=1, B=2, C=3, you will obtain

2

5. 2 = 23

3

The recipient of the message will obtain the sequence of numbers 14, 23, 18.

Write the sequence of numbers that will correspond to your entire message.

4

4

4. Use the Gauss-Jordan method to find the inverse of your matrix.

S

4

For example, if the original matrix is

2

4 5

6

3

7

2

-1/2 -1/121

its inverse will be

1/4

-5/24

0

1/6

Proper mechanics of writing

2

and APA compliance

5. Decode the sequence of numbers by left multiplying each 3-number group by the

Total

25

inverse matrix.

For example,