Let M2(R) be the set of 2 x 2 matrices with real entries. That is: {[: a b M2(R) = Let S2(R) be the set of 2 x 2 symmetric matrices with real entries. That is: S;(R) = {| T, y, z, w & y = Let D2(R) be the set of 2 x 2 diagonal matrices with real entries. That is: DAR) = {[; : mreR}. u 0 1. Prove that D2(R) C S2(R).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let M,(R) be the set of 2 x 2 matrices with real entries. That is:
M2(R) = {| : 1a, ,e, dER.
Let S2(R) be the set of 2 x 2 symmetric matrices with real entries. That is:
S-{R) = {|
{[:])
|1, y, z, w € R & y = z.
Let D2(R) be the set of 2 x 2 diagonal matrices with real entries. That is:
D:(R) = { , v ER.
1. Prove that D2(R) C S2(R).
2. Is S2(R) C D2(R)? Prove your answer.
Transcribed Image Text:Let M,(R) be the set of 2 x 2 matrices with real entries. That is: M2(R) = {| : 1a, ,e, dER. Let S2(R) be the set of 2 x 2 symmetric matrices with real entries. That is: S-{R) = {| {[:]) |1, y, z, w € R & y = z. Let D2(R) be the set of 2 x 2 diagonal matrices with real entries. That is: D:(R) = { , v ER. 1. Prove that D2(R) C S2(R). 2. Is S2(R) C D2(R)? Prove your answer.
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