-418Find the eigenvalues of A, given that A =3-6-4-1311-1and its eigenvectors are v1 =-1, V2 =and v3 =The corresponding eigenvalues are A1= -23and X2||

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Answered: 9. -4 18 Find the eigenvalues of A,…

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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4 6. If A= -4 2 -1 0 30-1 5 then find the eigenvalues of A.
4.- From the following 3x3 matrix, obtain the characteristic polynomial, the eigenvalues and the eigenvectors. [-6 -3 -25] 1 2 A = 2 2 8 87 7
4 3. Find eigenvalues an eigenvector of A = 2 0 -4 2 -2 2 0 1
4. Let -8 A = 1 1 Answer the following questions: (a) Find the eigenvalues, and bases for the eigenspaces. (b) Is A diagonalizable? If yes, find the matrix P that diagonalize A. Further, find A100.
5. Is 4 -3 1 an eigenvector of 3 -4 2 79 -5 1? If so, find the eigenvalue. 44
3. Let 12 -6 A = |-3 -10 -3 -12 8 Find the eigenvalues and eigenvectors of A.
4) Determine whether the given set of functions is linearly independent on the interval (-x,). a) (z) = cos 2z, (2) = 1, 1,()= cos z b) (z)=z, 1,(2)=z-1, (z)=z+3 c) ()=e**, 1,(=)=e
4. Find the eigenvalues and a basis for each eigenspace in C². Show all of the work (no calculator). -2 [13] 2
Verify that A is an eigenvalue of A and that x, is a corresponding eigenvector. 4 -2 = -11, x; = (1, 2, –1) 22 = -3, x, = (-2, 1 0) 23 = -3, x; = (3, 0, 1) A = 2 -7 6 2 4 -2 13 Ax- 2 -7 6. 2 -11 2 !! 2 4 -2 2 AX2 -2 -7 !! %3D !! 4 -2 AX3 2 -7 = 13x3 1
5) Find the values of that such that the given equations have non-trivial solutions. What are the eigenvalues and eigenvectors? (1-2) x + 2y = 0 2x + (4-2)y=0
Find the eigenvalues and the eigenvectors of A and A-1 (check the trace!): A λι = X2 = 2 A-1 = [ -0.5 11 0.5 ]: λι = with x1 = and 9. with x2 = with x1 = and 9. X2 = with x2 =
(b) Let C³ - - 1²: B = 1 c² C-3 0 0 с -C² ³+1 " where ce R. How many eigenvalues does B have and with what ge- ometric multiplicities? Without knowing c, is it possible to determine whether B is diagonalizable? Explain your answers.

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9. -4 18 Find the eigenvalues of A, given that A 3 -6 -4 4 -13 1 1 and its eigenvectors are v1 = -1 , V2 = and v3 = The corresponding eigenvalues are A1 ,A2 = -23 %3D %3D and X2