For an irreducible polynomial p(X) = 1+X + X² € F[X] consider F4 generated by p(X). Find x1, x2 E F, such that [10] × x1 + [11] × x2 = [01] (01] x x1 + [01] x x2 = [10]. Express x1 and x2 in vector form of length 2, e.g., (00].
For an irreducible polynomial p(X) = 1+X + X² € F[X] consider F4 generated by p(X). Find x1, x2 E F, such that [10] × x1 + [11] × x2 = [01] (01] x x1 + [01] x x2 = [10]. Express x1 and x2 in vector form of length 2, e.g., (00].
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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M4
![For an irreducible polynomial p(X)=1+X +
X² e F2[X] consider F4 generated by p(X).
Find x1, x2 E F4 such that
[10] x x1 + [11] × x2 = [01]
(01] x x1 + [01] × x2 = [10].
Express r1 and x2 in vector form of length 2,
e.g., [00].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fb4bc67-5d6a-40d6-a872-72e7a1893aba%2F1441c540-279a-4fe8-9ce7-021cf5b69aa8%2Fu5roqy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For an irreducible polynomial p(X)=1+X +
X² e F2[X] consider F4 generated by p(X).
Find x1, x2 E F4 such that
[10] x x1 + [11] × x2 = [01]
(01] x x1 + [01] × x2 = [10].
Express r1 and x2 in vector form of length 2,
e.g., [00].
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