**Problem 2: Modular Arithmetic Computation**If \( a \equiv 3 \pmod{11} \) and \( b \equiv 9 \pmod{11} \), compute the values, positive and fully-reduced modulo the modulus:(a) Compute \( 2a + b \pmod{11} \)(b) Compute \( (a - b)^2 \pmod{11} \)---This problem involves determining expressions in modular arithmetic, specifically modulo 11. Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value, the modulus. The goal is to simplify expressions using given equivalences and compute the results within the defined modulus.

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Answered: 2. If a = 3 (mod 11) and b = 9 (mod…

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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Refer to image
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2. If a = 3 (mod 11) and b = 9 (mod 11), compute the values, positive and fully-reduced modulo the modulus: (a) Compute 2a + b (mod 11) (b) Compute (a - b)² (mod 11)