Do all partsASAPI vll upvote for good solution Let1 2A =2E M2(Q).Define a ring homomorphism$: Q[r] →→ M2(Q),f(x) → f(A).(i) Show that A² – 2A – 3 = 0.(ii) Show thatker(ø) = (x? – 2x – 3).(iii) Find a pair of zero divisors in the image of ø.

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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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 4E: [Type here] Examples 5 and 6 of Section 5.1 showed that is a commutative ring with unity. In...

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Do all parts ASAP I vll upvote for good solution

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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