. Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) : AT=—A}. (a) Show: 1 01 0 (6₂9). 6 ) ( )). ·((i+¹)). 1 (i.) U₁ = span (ii.) U₂ = spanⓇ (iii.) M₂ (R) = spang 0 1 (CD) - C D) G J). A)). 0 10 1 0
. Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) : AT=—A}. (a) Show: 1 01 0 (6₂9). 6 ) ( )). ·((i+¹)). 1 (i.) U₁ = span (ii.) U₂ = spanⓇ (iii.) M₂ (R) = spang 0 1 (CD) - C D) G J). A)). 0 10 1 0
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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Transcribed Image Text:2. Consider M₂ (R) as a vector space and its subspaces U₁ = {A € M₂(R): AT = A}
and U₂= {A € M₂(R) : AT =−A}.
(a) Show:
(69) (
(ii.) U₂ = spanⓇ ((¹))
(iii.) M₂(R) = spang
(i.) U₁
=
spanⓇ
0
-9) (1 :)).
9
1
0
0
0
(6.1). ( ). (i ) ( )).
9
01
0
1
1
0
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