(Part 1)
(Part 1)
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=== Part 1 ===
 
=== Part 1 ===
  
All Bob has to do to decrypt his message is:
+
All Bob has to do to decrypt his message is:<br>
1. Take the "message" vector and divide it into columns with three rows, such that the first, second, and third elements are in the first column, the fourth, fifth, and sixth elements are in the second column, etc.
+
1. Take the "message" vector and divide it into columns with three rows, such that the first, second, and third elements are in the first column, the fourth, fifth, and sixth elements are in the second column, etc.<br>
2. Multiply the inverse of the "special" matrix that she sent him with each segment of the message vector.   
+
2. Multiply the inverse of the "special" matrix that she sent him with each segment of the message vector.  <br>
3. Combine all the segments in the correct order
+
3. Combine all the segments in the correct order <br>
4. Convert the numbers back to letters using Alice's system such that A=1, B=2...
+
4. Convert the numbers back to letters using Alice's system such that A=1, B=2...<br>
  
 
That's it!
 
That's it!

Revision as of 13:06, 16 September 2008

Application of Linearity

Part 1

All Bob has to do to decrypt his message is:
1. Take the "message" vector and divide it into columns with three rows, such that the first, second, and third elements are in the first column, the fourth, fifth, and sixth elements are in the second column, etc.
2. Multiply the inverse of the "special" matrix that she sent him with each segment of the message vector.
3. Combine all the segments in the correct order
4. Convert the numbers back to letters using Alice's system such that A=1, B=2...

That's it!

Part 2

Part 3

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett