PLEASE answer part 7 only for this problem. Please give clear steps and explanations. Modulo 26 ArithmeticIn 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 example15 + 74 is the reminder of 89 after it is divided by 26. In particular, 15 + 74 = 11. The same worksfor multiplication.1. Find 13 + 24Give Arel cA2. Find 4 14thewith3. 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?%3D5. 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 suchelements, invertible modulo 26.7. What is a criteria to decide whether a matrix is invertible in modulo 26 algebra? Perhaps youcan run some 2 x 2 examples and analyze the matrices6 35 22 2131313which one is invertible?

Answered: 7. What is a criteria to decide whether…

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 9. 3 3 3 which one is invertible?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.6: Permutations

Problem 33E

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PLEASE answer part 7 only for this problem. Please give clear steps and explanations.

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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