=1²2²₂2=1 Consider A = Find the spectral decomposition of A. Show your work. b. Make a diagram showing the spectral decomposition of A as applied to the vector x = [2]. That is, show how Ax is a sum of the scaled projections of on the two eigenspaces. (This is similar to the diagram that was made in the lecture.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Consider A =
a.
[2²₂2 =3)
-2
Find the spectral decomposition of A. Show your work.
b. Make a diagram showing the spectral decomposition of A as applied to the vector x = [13].
That
is, show how Ax is a sum of the scaled projections of x on the two eigenspaces. (This is similar to
the diagram that was made in the lecture.)
Transcribed Image Text:2. Consider A = a. [2²₂2 =3) -2 Find the spectral decomposition of A. Show your work. b. Make a diagram showing the spectral decomposition of A as applied to the vector x = [13]. That is, show how Ax is a sum of the scaled projections of x on the two eigenspaces. (This is similar to the diagram that was made in the lecture.)
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