21 2:11 + + 7. When does the system 2ac2 = 612 + ax3 = -8.02 + 4ax3 = 0 0 have a nontrivial solution? 0 A) When a = 0 or a = 2. B) For any real number a. C) When a=0. D) When a = 0 or a = -2.

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mdasfaaruddinshareefLv10

18 Jul 2023

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3. Suppose that 2 and -5 are the only eigenvalues of the matrix A. Which of the following statements is true? A) 21 - A is invertible, and there is a nontrivial solution to Av = -5v. B) 21 - A is not invertible, and there is a nontrivial solution to Av = -5v. C) det(21 + A) = det(51 – A) = 0. D) det(21 + A) = 0, and there is a nontrivial solution to (51 – A)v = 0.

7. Suppose that 4 and -2 are the only eigenvalues of the matrix A. Which of the following statements is true? (a) 41-A is invertible, and there is a nontrivial solution to Av = -2v. (b) det (41+ A) = det(21 - A) = 0. (c) 41 - A is not invertible, and there is a nontrivial solution to Av = -2v. (d) det(41+ A) = 0, and there is a nontrivial solution to (21 - A)v = 0. (e) none of the above

1. Suppose that 4 and -1 are the only eigenvalues of a 2 x 2 matrix A. Which one of the following statements is true? A) 41 - A is invertible, and there is a nontrivial solution to Av = -v. B) 41 - A is not invertible, and there is a nontrivial solution to Av = v. C) det(41+ A) = det(-I + A) = 0. (D) det(41 - A) = 0 and rank(A + 1) = 1. E) None of the above.

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21 2:11 + + 7. When does the system 2ac2 = 612 + ax3 = -8.02 + 4ax3 = 0 0 have a nontrivial solution? 0 A) When a = 0 or a = 2. B) For any real number a. C) When a=0. D) When a = 0 or a = -2.

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