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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).

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).

Advanced Engineering Mathematics
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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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.
Transcribed Image Text: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).
Transcribed Image Text: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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