1. Consider the set of upper triangular 2 x 2 matrices, with real entries: b B = {(" "); GAVER} a, b, Then B is a ring, and in fact it is a subring of M₂2 (R). (You do not need to prove this.) Inside the ring B, consider the subset of strictly upper triangular matrices: Prove that U is an ideal in B. U-{()+DER} : =

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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1. Consider the set of upper triangular 2 × 2 matrices, with real entries:
a
{(1) MANER}
: a, b, de R
B
Prove that U is an ideal in B.
=
Then B is a ring, and in fact it is a subring of M₂(R). (You do not need to prove this.)
Inside the ring B, consider the subset of strictly upper triangular matrices:
-{()+DER}
:
Transcribed Image Text:1. Consider the set of upper triangular 2 × 2 matrices, with real entries: a {(1) MANER} : a, b, de R B Prove that U is an ideal in B. = Then B is a ring, and in fact it is a subring of M₂(R). (You do not need to prove this.) Inside the ring B, consider the subset of strictly upper triangular matrices: -{()+DER} :
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