Let A be an 5 by 5 matrix, let v₁ be an eigenvector of A with eigenvalue X₁ and let V₂ be an eigenvector of A with eigenvalue X₂. Select all items below that are true. D. For any real number c, cA₁ is also an eigenvalue of A.E. If 0 is an eigenvalue of A, then A is singular.F. If À₁ = №₂, then v₁ + v₂ is an eigenvector of A (as long as it is nonzero).

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Answered: D. For any real number c, cA₁ is also…

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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Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = 12 = -3, x2 = (-2, 1 0) 13 = -3, x3 = (3, 0, 1) -1 4 -6 (1, 2, –1) A = 4 5 -12 -2 -4 3 -1 4 -6 1 Ax1 = 4 5 -12 2 13 2 -2 -4 3 -1 -1 -1 4 -6 2 2 Ax2 4 5 -12 1 = -3 1 12x2 -2 -4 3 -1 4 -6 3 3 Ax3 = 4 5 -12 -3 13×3 -2 -4 3 1
If v1,v2, and v3 are linearly independent eigenvectors of A corresponding to the eigenvalue λ, and c1,c2, and c3 are scalars (not all zero), show that c1v1+c2v2+c3v3 is also an eigenvector of A corresponding to the eigenvalue λ.
Find the eigenvalues of A, given that A = and its eigenvectors are The eigenvalues are 5 -4 14 -6 3 -14 2 -818-8 and 3 -3 4 -12 2 -2 and
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I. Find the eigenvalues, eigenvectors, eigenspaces and bases for the eigenspaces for A. Determine the algebraic and geometric multiplicity of each eigenvalue. Show all work!! 1 A = -1 1 3
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D. For any real number c, cA₁ is also an eigenvalue of A. E. If 0 is an eigenvalue of A, then A is singular. F. If A₁ A₂, then v₁ +V₂ is an eigenvector of A (as long as it is nonzero).