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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Which of the following statements are correct?
a) A square matrix A is not invertible if and only if A = 0 is an eigenvalue of A.
b) If vị and v2 are linearly independent eigenvectors of a matrix A, then they correspond to different
eigenvalues.
c) If a square matrix A is triangular, then the eigenvalues of A are the entries on its main diagonal.
5 -4
8 -7
d) A= 5 is an eigenvalue of A
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- Let A be an n x n matrix.Which of the following statements is (are) true? Ⓒa) If Ax = Ax for some scalar A, the x is an eigenvector of A Statements b and d Statements a, b and d b)lf v₁ and v₂ are linearly independent eigenvectors, then they correspond to distinct eigenvalues Statements a, c and d Oc)An eigenspace of A is a null space of a certain matrix Statements cand d d)if A² is a zero matrix, then the only eigenvalue of A is 0arrow_forwardDetermine whether the eigenvalues of each matrix are distinct real, repeated real, or complex. -7 -8] 5 -6] -2 -4 -19 6 -36 11 46 -78 1 -6 - 26 -45 ? ? ? ?arrow_forward
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