1) The inverse of x' is: 2) The value that replaces x* is a) x+1 a) x+1 b) x² +1 b) x² +1 c) x c) x d) x d) x 4) An idempotent element in 5) The ring Z:[x]is:
1) The inverse of x' is: 2) The value that replaces x* is a) x+1 a) x+1 b) x² +1 b) x² +1 c) x c) x d) x d) x 4) An idempotent element in 5) The ring Z:[x]is:
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Question
factor ring part 1 2
![Table 1: Multiplication in Za[z]/ {r° + 1)
2+z+1 r² +z__z+1 ²+1
7+x+1 x* +I x+1 r*+1
+z+1 r +1 r²+z z+1
² +x+1 r+1 2+1 r+x
1
z* +z+1 +z+1 r*+z+1 r²+z+1 r*+z+1
2+1
+z z+1 r² +1
z+1 r²+1 r² +z
+1 +z z+1
z+1
+ 2+1
z+1
2+1
z+1
2 +1
z+1
1) The inverse of x' is:
2) The value that replaces xª is
3) (x² +1)* is equal to
a) x+1
а) х +1
а) х +1
b) x +1
b) x? +1
b) x+1
c) x
c) x
c) x
d) x
d) x2
d) x
4) An idempotent element in
5) The ring Z;[x]/< x³ +1 > is:
Z[x]/< x³ +1 >is:
a) Non-commutative ring
а) х
with identity
b) x?
b) Integral Domain
c) x+x+1
c) Field
d) 1+x
d) None
a
b
d
1)
2)
3)
4)
5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5f7d193-f615-43b0-941c-bc65ebfa4491%2Fdc023496-779c-465c-a1bf-c6050191aa09%2F54865ci_processed.png&w=3840&q=75)
Transcribed Image Text:Table 1: Multiplication in Za[z]/ {r° + 1)
2+z+1 r² +z__z+1 ²+1
7+x+1 x* +I x+1 r*+1
+z+1 r +1 r²+z z+1
² +x+1 r+1 2+1 r+x
1
z* +z+1 +z+1 r*+z+1 r²+z+1 r*+z+1
2+1
+z z+1 r² +1
z+1 r²+1 r² +z
+1 +z z+1
z+1
+ 2+1
z+1
2+1
z+1
2 +1
z+1
1) The inverse of x' is:
2) The value that replaces xª is
3) (x² +1)* is equal to
a) x+1
а) х +1
а) х +1
b) x +1
b) x? +1
b) x+1
c) x
c) x
c) x
d) x
d) x2
d) x
4) An idempotent element in
5) The ring Z;[x]/< x³ +1 > is:
Z[x]/< x³ +1 >is:
a) Non-commutative ring
а) х
with identity
b) x?
b) Integral Domain
c) x+x+1
c) Field
d) 1+x
d) None
a
b
d
1)
2)
3)
4)
5)
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