262. Let R = {a + bv2 | a, b e Z} and let R' consist of all 2 by 2 matrices of the formOn the last homework, you showed R was a ring (in fact it is a subring of R). Show that Ris a subring of Mat2(Z). Then show that p: R R' defined bya26p(a + bv2)ais an isomorphism.

Given set is R'=a2bba:a,b∈ℤ To prove that R' is a subring of M2ℤ It is known that a non-empty…

2. Let R = {a + bv2 | a,b e Z} and let R' consist of all 2 by 2 matrices of the form On the last homework, you showed R was a ring (in fact it is a subring of IR). Show that R' is a subring of Mat2(Z). Then show that p: R R' defined by 26 p(a + bv2) = ( ) %3D is an isomorphism.

2. Let R = {a + bv2 | a,b e Z} and let R' consist of all 2 by 2 matrices of the form On the last homework, you showed R was a ring (in fact it is a subring of IR). Show that R' is a subring of Mat2(Z). Then show that p: R R' defined by 26 p(a + bv2) = ( ) %3D is an isomorphism.

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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26
2. Let R = {a + bv2 | a, b e Z} and let R' consist of all 2 by 2 matrices of the form
On the last homework, you showed R was a ring (in fact it is a subring of R). Show that R
is a subring of Mat2(Z). Then show that p: R R' defined by
a
26
p(a + bv2)
a
is an isomorphism.

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