For each of the following, determine if the statement is true or false. Provide a short reasoning (one or two sentences). a) If v is an eigenvector of a square matrix A with corresponding eigenvalue A, then 20 is also an eigenvector of a square matrix A with corresponding eigenvalue d. b) If the characteristic polynomial of a square matrix has a nonzero constant term, then the matrix is invertible. c) If an eigenvalue of a square matrix has algebraic multiplicity 1, then the dimension of the associated eigenspace is 1.

For each of the following, determine if the statement is true or false. Provide a short reasoning (one or two sentences). a) If v is an eigenvector of a square matrix A with corresponding eigenvalue A, then 20 is also an eigenvector of a square matrix A with corresponding eigenvalue d. b) If the characteristic polynomial of a square matrix has a nonzero constant term, then the matrix is invertible. c) If an eigenvalue of a square matrix has algebraic multiplicity 1, then the dimension of the associated eigenspace is 1.

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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Question

For each of the following, determine if the statement is true or false. Provide a short
reasoning (one or two sentences).
a) If v is an eigenvector of a square matrix A with corresponding eigenvalue A, then
20 is also an eigenvector of a square matrix A with corresponding eigenvalue d.
b) If the characteristic polynomial of a square matrix has a nonzero constant term,
then the matrix is invertible.
c) If an eigenvalue of a square matrix has algebraic multiplicity 1, then the dimension
of the associated eigenspace is 1.

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