III) Consider 1 1 3 A = -1 1 4 0 0 2) Which one of the following statements is true? a) 1 is an eigenvalue of A. b) i is an eigenvalue of A. c) 1+i is an eigenvalue of A. d) v2 is an eigenvalue of A. e) None of the above.

III) Consider 1 1 3 A = -1 1 4 0 0 2) Which one of the following statements is true? a) 1 is an eigenvalue of A. b) i is an eigenvalue of A. c) 1+i is an eigenvalue of A. d) v2 is an eigenvalue of A. e) None of the above.

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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Question

I) In R², equipped with its Euclidean product, consider the plane L = Span(p) spanned
()-
by p=
If u =
and PL(u) = 2p, what is the value of b.
II) Consider R with its Euclidean inner product. If M is the span in R' of the
following 4 vectors
what is the dimension of M+?
III) Consider
1
1 3
A = -1 1 4
0 02
. Which one of the following statements is true?
a) 1 is an eigenvalue of A.
b) i is an eigenvalue of A.
c) 1+i is an eigenvalue of A.
d) v2 is an eigenvalue of A.
e) None of the above.
IV) Consider
V3
A =
V3
2
2
Which one of the following statements is true?
a)
is an eigenvector of A.
b)
is an eigenvector of A.
V3
c)
is an eigenvector of A.
3
d)
is an eigenvector of A.
V3
2
e) None of the above.

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