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Modulo 26 Arithmetic In this part of the project, we will learn what is arithmetic and linear algebra modulo 26. Now, because we have only 26 numbers, arithmetic works via reminders, which means that, for example 15 + 74 is the reminder of 89 after it is divided by 26. In particular, 15 +74 = 11. The same works for multiplication. 1. Find 13 + 24 2. Find 4 14 3. Can you find a number r such that 3x = 1 modulo 26?

Modulo 26 Arithmetic In this part of the project, we will learn what is arithmetic and linear algebra modulo 26. Now, because we have only 26 numbers, arithmetic works via reminders, which means that, for example 15 + 74 is the reminder of 89 after it is divided by 26. In particular, 15 +74 = 11. The same works for multiplication. 1. Find 13 + 24 2. Find 4 14 3. Can you find a number r such that 3x = 1 modulo 26?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Modulo 26 Arithmetic In this part of the project, we will learn what is arithmetic and linear algebra modulo 26. Now, because we have only 26 numbers, arithmetic works via reminders, which means that, for example 15 + 74 is the reminder of 89 after it is divided by 26. In particular, 15 + 74 = 11. The same works for multiplication. 1. Find 13 + 24 Give Arel cA 2. Find 4 14 the with 3. Can you find a number x such that 3x = 1 modulo 26? 4. Can you find a number x such that 2x = 1 modulo 26? %3D 5. Can you find a number x such that 13x = 1 modulo 26? 6. List all the numbers a such that you can find an x such that ax = 1 modulo 26? call such elements, invertible modulo 26. 7. What is a criteria to decide whether a matrix is invertible in modulo 26 algebra? Perhaps you can run some 2 x 2 examples and analyze the matrices 6 3 5 2 2 2 1 3 1 3 1 3 which one is invertible?
Transcribed Image Text:Modulo 26 Arithmetic In this part of the project, we will learn what is arithmetic and linear algebra modulo 26. Now, because we have only 26 numbers, arithmetic works via reminders, which means that, for example 15 + 74 is the reminder of 89 after it is divided by 26. In particular, 15 + 74 = 11. The same works for multiplication. 1. Find 13 + 24 Give Arel cA 2. Find 4 14 the with 3. Can you find a number x such that 3x = 1 modulo 26? 4. Can you find a number x such that 2x = 1 modulo 26? %3D 5. Can you find a number x such that 13x = 1 modulo 26? 6. List all the numbers a such that you can find an x such that ax = 1 modulo 26? call such elements, invertible modulo 26. 7. What is a criteria to decide whether a matrix is invertible in modulo 26 algebra? Perhaps you can run some 2 x 2 examples and analyze the matrices 6 3 5 2 2 2 1 3 1 3 1 3 which one is invertible?
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