MatriceA) show that if Ais Kal Syomnestric V, then NANequals to the larggest Eigen Value of ANor MS Ore induction and defred as: 1Al, = max(.= Max (LAR)b) Assume A and A as below :9.-4-1713 -177A= 13 29 -386.A=-4-17 5ヒげー850and Eigenvalues e A arealro ximately 84.7405, 0.2007 and0.0588 . Referng to Previous Perragra Ph calculate HAR HAl and cataC)Ass me Vectors a and x extst such thab AR-b anal Ilb-AllF6?Referng to Previous Para graph find UPler bound of 1X-Abl andU-AbMA L

(a) If A is a real symmetric matrix, then we have to prove that A equals to the largest eigen value…

Answered: A) show that if Ais a real symmetric,…

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-) a) What matrices are called similar? Show that the eigenvalues of a matrix A satisfying Ax = Ax remains the same eigenvalue under a similarity transformation. b) Find A° for A = l6 by using the advantage of the diagonal representation by similarity transformation.
1 Let An be the nx n matrix with = ai, i 2 (i=1 to n), ai,i+1 = 1 (i = 1, 2,..., n 1), ai+1,i = -1 (i=1,2,..., n-1) and all other induction on n that aij = 0. Show by det(An) = √²[(1 + √2)”+¹ − (1 − √√2)~+¹] - What is da? [Hint: use expansion along row/down column to get an expression for dn in terms of dn-1 and dn-2.]
Show that lambda of wilks, which is |E|/|B + E\, can be expressed as lambda = || II i=1 where d1, · · , Agis eigen value of E-1B
3. If A = 0 -1 0then the bases for the eigenspaces of A2 + 21 are: 2. a) ({, = 7, v, = (1,0,0), {A2 = 4, v (-1,0,1)}, and (A = 1, v, = (-1,6,0}) b) {{ =-3, v, = (-1,6,0}), (A = 3, v (1,0,0}}, and (A = 0, v, = (1,0,0}] c) [{ = 27, v, = (1,0,0},{22 = 6, v = (-1,0,1}}, and (As = 3, s =(-1,6,0}} d) {{2 = 2, v, ={-1,0,1}}. [A2 = 23, , = [1,0,0), and (As =-1,, {-1,6,0}}
Section 5.1:4(d) only correctly!!
What t The Aie Lue genspace what is the dimension of the eigenpace o The Following marix? + Good handwritting 53 Please.
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 0 ^= (-2) A 9). a) The characteristic polynomial is p(r) = det(A - rI) = (r+3)(r-4) b) List all the eigenvalues of A separated by semicolons. -3;4 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. ab sin (a) ∞ a ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. 08 f C X
The eigenvalues of a symmetric L2 – kernel form a finite or an infinite sequence (A„) with no finite limit poin

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