for the coefficients. 0 1 2 8 0 x + 1 0 x + 2 0 2x 0 2x + 1 0 2x + 2 0 0 2 X 1 X+1 X+2 2x 2x+1 2x+2 0 2 2x 2x+2 2x+1 X X+2 2 X+1 0 X 8 2x 2x+1 X+1 X+2 2x+2 2 0 x + 1 X+1 2x+2 1 X+2 2x 2 X 2X+1 0 x + 2 X+2 2x+1 X+1 2x 1 2x+2 1 2x 0 2x X 2x X+2 2 2x+2 2X+1 X+1 1 2x + 1 0 2x+1 X+2 2x+2 X 1 X+1 2 2x 2x + 2 0 2x+2 X+1 2 2X+1 2x 1 2x X+2
for the coefficients. 0 1 2 8 0 x + 1 0 x + 2 0 2x 0 2x + 1 0 2x + 2 0 0 2 X 1 X+1 X+2 2x 2x+1 2x+2 0 2 2x 2x+2 2x+1 X X+2 2 X+1 0 X 8 2x 2x+1 X+1 X+2 2x+2 2 0 x + 1 X+1 2x+2 1 X+2 2x 2 X 2X+1 0 x + 2 X+2 2x+1 X+1 2x 1 2x+2 1 2x 0 2x X 2x X+2 2 2x+2 2X+1 X+1 1 2x + 1 0 2x+1 X+2 2x+2 X 1 X+1 2 2x 2x + 2 0 2x+2 X+1 2 2X+1 2x 1 2x X+2
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 29EQ: Write out the addition and multiplication tables for 4.
Related questions
Question
red boxes are wrong
![Let F3 = Z/3Z and consider the quotient ring F3[x]/(x² + 1). Complete the multiplication table in this ring. Use only the representatives 0, 1, 2
for the coefficients.
0
1
2
I
x + 1
x + 2
2x
2x + 1
2x + 2
0
0
0
0
0
0
0
1
2
X
X+1
1
X+2
2x
2x+1
2x+2
0
2
1
2x
2x+2
2x+1
X
2
X+2
X+1
X
2x
2x+1
1
X+1
X+2
R
2x+2
2
0
X+1
2x+2
1
x+1
X+2
2x
2
X
2x+1
0
x + 2
X+2
2x+1
X+1
2x
1
2x+2
1
2x
0
2x
X
2x
X+2
2
2x+2
2x+1
X+1
1
2x + 1
0
2x+1
X+2
2x+2
X
1
X+1
2
2x
2x + 2
0
2x+2
X+1
2
2x+1
2x
1
2x
X+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e903c09-c796-4754-aa19-01a5a83c6f2c%2Ff48ff29b-8b0c-4102-831d-242a6872b86b%2Fqyq0wio_processed.png&w=3840&q=75)
Transcribed Image Text:Let F3 = Z/3Z and consider the quotient ring F3[x]/(x² + 1). Complete the multiplication table in this ring. Use only the representatives 0, 1, 2
for the coefficients.
0
1
2
I
x + 1
x + 2
2x
2x + 1
2x + 2
0
0
0
0
0
0
0
1
2
X
X+1
1
X+2
2x
2x+1
2x+2
0
2
1
2x
2x+2
2x+1
X
2
X+2
X+1
X
2x
2x+1
1
X+1
X+2
R
2x+2
2
0
X+1
2x+2
1
x+1
X+2
2x
2
X
2x+1
0
x + 2
X+2
2x+1
X+1
2x
1
2x+2
1
2x
0
2x
X
2x
X+2
2
2x+2
2x+1
X+1
1
2x + 1
0
2x+1
X+2
2x+2
X
1
X+1
2
2x
2x + 2
0
2x+2
X+1
2
2x+1
2x
1
2x
X+2
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