a) Find a 2 × 2 matrix A such that (−4, 0) and (−2, −4) are eigenvectors of A corresponding eigenvalues 9 and −7. (b). Let B be the matrix [3 2 4 1] Find the eigenvalues and corresponding eigenvectors of B. c) Find the eigenvalue of C corresponding to the eigenvector (−1, 1, 0)^t (t stands for transposition) given that C is the matrix [10   5 − 9 −9  −4  9 5      5 −4]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a) Find a 2 × 2 matrix A such that (−4, 0) and (−2, −4) are eigenvectors
of A corresponding eigenvalues 9 and −7.

(b). Let B be the matrix
[3 2
4 1]

Find the eigenvalues and corresponding eigenvectors of B.

c) Find the eigenvalue of C corresponding to the eigenvector (−1, 1, 0)^t
(t stands for transposition) given that C is the matrix

[10   5 − 9
−9  −4  9
5      5 −4]

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Thank you!

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Please resubmit solution as this instuctions is very uneasy to understand

Where did all these values come from
part a)

Where  

                  P=-4-20-4  and  D=900-7

Now

                     P-1=1det(P)Adj(P)⇒P-1=116-420-4⇒P-1=18-210-2

Therefore

                  A=PDP-1⇒A=-4-20-4900-718-210-2⇒A=18-4-20-4-189014⇒A=1872-640-56⇒A=9-80-7

Hence the matrix

A=9-80-7

Please explain part a, b, c again i cant live with the previuos explanation. Thank you!!


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