A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If v, and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. Choose the correct answer below. O A. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because eigenvectors must be nonzero. O B. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because all eigenvectors of a single eigenvalue are linearly dependent. O c. The statement is false. There may be linearly independent eigenvectors that both correspond to the same eigenvalue. O D. The statement is false. Every eigenvalue has an infinite number of corresponding eigenvectors.
A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If v, and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. Choose the correct answer below. O A. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because eigenvectors must be nonzero. O B. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because all eigenvectors of a single eigenvalue are linearly dependent. O c. The statement is false. There may be linearly independent eigenvectors that both correspond to the same eigenvalue. O D. The statement is false. Every eigenvalue has an infinite number of corresponding eigenvectors.
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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A is an n x n matrix. Determine whether the statement below is true or false. Justify the answer.
If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.
Transcribed Image Text:A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
If v, and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.
Choose the correct answer below.
O A. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because eigenvectors
must be nonzero.
O B. The statement is true. If v, and v, are linearly independent eigenvectors, then they correspond to distinct eigenvalues, because all
eigenvectors of a single eigenvalue are linearly dependent.
O c. The statement is false. There may be linearly independent eigenvectors that both correspond to the same eigenvalue.
O D. The statement is false. Every eigenvalue has an infinite number of corresponding eigenvectors.
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