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Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

Advanced Engineering Mathematics
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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10. Consider j,ỹ,, ÿ,ER° and that ý,+ỷ,+ỷ;=0. For Î=span{y,,y2} and Y=span{y2, y}, show that Î=Ỹ.
Transcribed Image Text:10. Consider j,ỹ,, ÿ,ER° and that ý,+ỷ,+ỷ;=0. For Î=span{y,,y2} and Y=span{y2, y}, show that Î=Ỹ.
Expert Solution
Step 1

Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0.

Let Y^=spany1→,y2→ and Y~=spany2→,y3→.

To show Y^=Y~, it is enough to show that both subspaces contains the basis or spanning vectors of other subspace.

Since  y2→ vector is common spanning vectors in both subspaces. Therefore it is enough to show that y1→∈Y~ and y3→∈Y^.

 

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