8. Let A and B are square matrices of the same order and let S non-singular matrix and Asimilar to B, such that A = S-¹BS. Then f2) = f(), where fB (A) = det (B-AI)and λ is an eigenvalue.O TrueO False

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Answered: 8. Let A and B are square matrices of…

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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2) Let A is 2 x 2 matrix with 4 and -3 eigenvalues and suppose that is an eigenvector for the value 4 and is an eigenvector for the value -3. Find A.
True/False: There exists a square real matrix A with no real eigenvalues. True False
Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is true if the columns of matrix A are a₁ = (1, -2, 0), a₂ = (-3, 4, 1), a3 = (-8, 6, 5), a4 = (-3, 0, 7) (3,3,1), Col A is a subspace of R³ O (3,1,3), Row A is a subspace of R³ O (1, 3,3), Row A is a subspace of R³ O (2,2,2), Nul A is a subspace of Rª O (3,3,1), Col A is a subspace of R¹ O (1,3,3), Row A is a subspace of R4 O (3, 1,3), Nul A is a subspace of Rª ○ None of the above
True/False: A non-zero sum of two eigenvectors of a matrix A is always an eigenvector. O True O False
If the eigenvalues of a matrix A are 1 = 3 and 2 = -1 which of the following are the eigenvalues of itsSA?matrix? O A) (3,1) O B) (-6,2) OC) (9,1) OD) (3,1) O E) (6,-2)
Let A E Rx2 be a matrix with (eigenvalue,eigenvectors) = {(2, V1), (–1, 02)}, where ð1 and U2 %3D Let w = 201 + V2 = Compute A w, and use the (eigenvalue,eigenvector) knowledge. W mk 000 000 F4 F3 F5 F6 F7 F8 F9 $ 4 % & * 6 7 R Y U F G H J K
Let f be the invertible linear transformation represented by the matrix -2 ^-(-²¹) A = 1). 4 4 Find, in terms of and y, the equation of the image f(C) of the unit circle C. The equation is
Matrix A (image) has the following set of eigenvectors: x1 = (1, 0,1), x2 = (0,1,0), and x3 = (-1, 0,1). One of the properties of the eigenvectors of Hermitian matrices is that their eigenvectors are orthonormal. Verify that this is the case for the eigenvectors of A.
-4 2] Given the matrix 4 the eigenvector is (b)
hon- singular matrix. Show that if Ato is en etgenvalue of of A-4. Let AcMunCIR) be a 1lA is an eigenvalue
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For the matrix A, find (if possible) a nonsingular matrix P such that P-!AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -3 A = -2 P = Verify that P-'AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

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8. Let A and B are square matrices of the same order and let S non-singular matrix and A similar to B, such that A = S-¹BS. Then f₁() = f(), where fB (A) = det (B-AI) and λ is an eigenvalue. O True O False