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### 11_11_concept_questions

Course: MATH 2940, Fall 2011
School: Cornell
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Questions: Concept 11-11-2011 MA2940: Linear Algebra for Engineers Diagonalization 1) (T/F) If = 0 is an eigenvalue of a square matrix A, then A is not diagonalizable. 2) (T/F) If 16 is an eigenvalue of A4 , then 2 is an eigenvalue of A. 3) (T/F) Suppose n n matrices A and B can be diagonalized with the same eigenvector matrix S . Then AB = BA. 4) (T/F) Suppose n n matrices A and B can be diagonalized, and AB...

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Questions: Concept 11-11-2011 MA2940: Linear Algebra for Engineers Diagonalization 1) (T/F) If = 0 is an eigenvalue of a square matrix A, then A is not diagonalizable. 2) (T/F) If 16 is an eigenvalue of A4 , then 2 is an eigenvalue of A. 3) (T/F) Suppose n n matrices A and B can be diagonalized with the same eigenvector matrix S . Then AB = BA. 4) (T/F) Suppose n n matrices A and B can be diagonalized, and AB = BA. Then they can be diagonalized with the same matrix S of eigenvectors. Applications to Dierential Equations 5) (T/F) It is possible to have eigenvalues = 1 2 that share the same eigenvector. 6) (T/F) It is possible to have eigenvectors v1 = v2 that share the same eigenvalue. 7) (T/F) Any matrix system tial equation. d u(t) dt = Au(t) an be written as a single higher-order dieren- 8) (T/F) If w(t) and v (t) are solutions to d u(t) dt = Au(t) + b, then w + v is a solution too. 9) (T/F) If a square matrix A is unstable, then tr(A) > 0 and det(A) < 0. d 10) When solving dt u(t) = Au(t), does it matter if A isnt diagonalizable? (Yes.) Why doesnt our method work? What do we do? TA: Kyle Wilson
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