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: (i.) U₁ = spang (ii.) U₂ 1 (69). 6). (15)). ·((i+¹)). = span (iii.) M₂ (R) = spang 1 0 0 0 (6 ) ( ) ( ) ( ¹)). 7 0 -
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: (i.) U₁ = spang (ii.) U₂ 1 (69). 6). (15)). ·((i+¹)). = span (iii.) M₂ (R) = spang 1 0 0 0 (6 ) ( ) ( ) ( ¹)). 7 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: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:
(i.) U₁ = spang
(ii.) U₂
= span
1
(69) 69). (i)).
·((i+¹)).
1 0
2 (69) 6 9 ). ( ). (id)).
(iii.) M₂ (R) = spang
(b) For any matrix A € M₂ (R), show that we can uniquely write A = A₁ + A₂
with A₁ € U₁ and A₂ € U₂.
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