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Question: i 2 guestions marks a matrix a has the eigenvalues...

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i. (2 guestions marks) A matrix A has the eigenvalues -2, 7 and 5. Which of the followi (A) The condition number of A based on the spectral norm is (C) the spectral norm of A is 7 is true: ng statements (D) None of (A)-(C) are true. ANSWER: 11. 12. (2 marks) Using Gaussian 2-point quadrature, the estimate for the integral sin r dr is best estimated to be (A) 0 (B) approximately 0.459588 (C) approximately 0.0087264 (D) None of (A)-(C) are true. ANSWER: 12. 13. (2 marks) Consider a second-order accurate finite-difference approximation for 1(2) for f(z) = e-z + 4, and let E be the maximum true error when using h 0.5. Which of the following statements is true: (A) the maximum, true error is expected to be E/4 when using h = 0.25 (B) nothing can be said about the maximum true error when h 0.25 (C) the maximum true error is expected to be E/2 when using h 0.25 (D) None of (A)-(C) above ANSWER: 13. 14. (2 marks) The result of the following commands entered in Matlab: x [-1 2 4] y [-2 1 5] polyfit(x,y,2) is ans 0.2000 0.8000 -1.4000 Which of the following statements is true (A) the best quadratic polynomial fitting the data is 0.2+0.8x -1.422 (B) the best quadratic polynomial fitting the data is -148+0.2r (C) the best straight line fitting the first 2 data points is 0.2+0.8r which evaluates to -1.4 when (D) None of (A)-(C) are true ANSWER: 14.
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