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Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=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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Consider ỹ,,y2, ÿ,ER³ and that y, +y,+y,=0. For Î=span{ỹ,,y,} and Y=span y2, ya}, show that Î=Ỹ.
Transcribed Image Text:Consider ỹ,,y2, ÿ,ER³ and that y, +y,+y,=0. For Î=span{ỹ,,y,} and Y=span y2, ya}, show that Î=Ỹ.
Expert Solution
Step 1

Given  that  y→1, y→2, y→3∈ℝ5 and that

                  y→1+ y→2+ y→3=0→.

and           Y^=spany→1, y→2 and Y~=spany→2, y→3.

 

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