Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Suppose a system of differential equations yields eigenvalue λ=1+3i with 2+i eigenvector = Find any real-valued solution.
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Transcribed Image Text:Suppose a system of differential equations yields eigenvalue λ=1+3i with 2+i eigenvector = Find any real-valued solution.
Expert Solution
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Step 1: Determine the given variables

Given space that The space eigen space value space space straight lambda subscript 1 equals 1 plus 3 i space This space is space in space the space form space lambda subscript 1 equals alpha plus beta i Here space space alpha equals 1 space space comma space space beta equals 3 The space eigenvector space omega with rightwards arrow on top equals open square brackets table row cell 2 plus i end cell row 1 end table close square brackets equals open square brackets table row 2 row 1 end table close square brackets plus straight i open square brackets table row 1 row 0 end table close square brackets This space is space in space the space form space omega with rightwards arrow on top equals u subscript 1 plus i u subscript 2 Here space space u subscript 1 equals open square brackets table row 2 row 1 end table close square brackets space space comma space space u subscript 2 equals open square brackets table row 1 row 0 end table close square brackets

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