Linear Algebra October 2017 var1-4.pdf

# Linear Algebra October 2017 var1-4.pdf - Linear Algebra...

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Linear Algebra, Final Exam 2017 I. All eigenvalues of A are non-zero II. Eigenvectors that correspond to the same eigenvalue are linearly dependent III. Eigenvectors that correspond to different eigenvalues are linearly independent 6. Let A be a matrix such that A n = 0 for some n > 0 (such a matrix is called nilpotent ). Which of the following MUST be true? I. λ = 0 is an eigenvalue of A II. A doesn’t have eigenvalues other than λ = 0 III. If A is diagonalizable, then A = 0 (A) I only (B) I and II (C) I and III (D) II and III (E) I, II, and III
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