4.-22A = 222 -2 4In this assignment, we will diagonalize A.STEP 1:Solve the characteristic equation det(A – AI3) = 0 to find the eigenvalues and theirmultiplicities.Answer:The smaller one is à1 =with multiplicityThe other (the larger one) is d2=with multiplicityReminder: λι < λ .

Answered: Image /qna-images/answer/3d228b90-b7b7-49c3-adf0-7c985ec5672a.jpg

Answered: 4. -2 2 A = 2 2 -2 4 In this…

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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Use (a) to solve the system x = (: :) . Х. -8 7 NB: Real solutions are required. Hint: Recall that if the roots of C(A) = 0 occur in complex conjugate parts, then any one of the two eigenvalues yields two linearly independent solutions. The second will yield solutions which are identical (up to a constant) to the solutions already found. a) is as follows Show from first principles, i.e., by using the definition of linear independence, that if x+iy, y # 0 is an eigenvalue of a real matrix A with associated eigenvector v = u + iw, then the two real solutions Y(t) = et (u cos bt – w sin bt) and Z(t) = eat (u sin bt + w cos bt) are linearly independent solutions of X = AX.
You need to check your QR factorization code using a simple matrix. Use the characteristic equation to solve for the eigenvalues by hand. 3 [9] -1
Q: Conficm by multiplicationthel cingenvector" of A, and find the collesponding l an eigenvalve. 1 2. 2. %3D 2.
Thank you for your response, the calculations are clear up to factoring using the quadratic equations. however, I do not understand the concept behind for which values of k does A have two distinct real eigenvalues and when is there no real eigenvalues from the response. Please explain. Thank you
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.
Please answer thank you
How to solue X-2 by iteration? %3D X+2
Sec(3.5) Uh need to solve all parts kindly of q2 And take a thumb up plz and solve correctly
Please answer quickly

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4. -2 2 A = 2 2 -2 4 In this assignment, we will diagonalize A. STEP 1: Solve the characteristic equation det(A – AI3) = 0 to find the eigenvalues and their multiplicities. Answer: The smaller one is à1 = with multiplicity The other (the larger one) is 12= with multiplicity Reminder: À1 < d2.