The set of matrices of the form- {:mnR =m, n E2n тforms a subring of M2(Z). Prove that R is isomorphic to the ring Z[V2] = {m+n/2 |m, n E Z}.

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The set of matrices of the form {[ m n | m,n € Z} R 2n m forms a subring of M2 (Z). Prove that R is isomorphic to the ring Z[V2] = {m+ ny2 |m,n E Z}.

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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Question

The set of matrices of the form
- {:
m
n
R =
m, n E
2n т
forms a subring of M2(Z). Prove that R is isomorphic to the ring Z[V2] = {m+
n/2 |m, n E Z}.

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