Let A e M2(Q). 2 Define a ring homomorphism ф: Q] —> М2(Q), f(x) → f(A). (i) Show that A² – 2A – 3 = 0. (ii) Show that ker(ø) = (x² – 2.x – 3). (iii) Find a pair of zero divisors in the image of ø.
Let A e M2(Q). 2 Define a ring homomorphism ф: Q] —> М2(Q), f(x) → f(A). (i) Show that A² – 2A – 3 = 0. (ii) Show that ker(ø) = (x² – 2.x – 3). (iii) Find a pair of zero divisors in the image of ø.
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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![Let
1 2
A =
2
E M2(Q).
Define a ring homomorphism
$: Q[r] →
→ M2(Q),
f(x) → f(A).
(i) Show that A² – 2A – 3 = 0.
(ii) Show that
ker(ø) = (x? – 2x – 3).
(iii) Find a pair of zero divisors in the image of ø.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fceb54a1e-6a60-4744-9db1-8508c0c7ded7%2F2badd465-7679-4f47-a463-296c8b31a17c%2F1c7i42_processed.png&w=3840&q=75)
Transcribed Image Text:Let
1 2
A =
2
E M2(Q).
Define a ring homomorphism
$: Q[r] →
→ M2(Q),
f(x) → f(A).
(i) Show that A² – 2A – 3 = 0.
(ii) Show that
ker(ø) = (x? – 2x – 3).
(iii) Find a pair of zero divisors in the image of ø.
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