State and Prove the diggonally dominentCondibion af convergence of Guass -Jacobiaund Gauss - Siedel method.i, eElaijl <1T ail

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Answered: State and Prove the diagonaliy dominent…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Prove or disprove these two statements: (i) if ƒ is Riemann integrable on [a, b] then so is |ƒ|. (ii) if |ƒ| is Riemann integrable on [a, b] then so is f. (Hint: Try a slight modification of the Dirichlet function as a potential counterexample).
23) Find the constants a. B if the value of integration (ax³-B)dx n=2 by trapezoidal rule and Simpson 1/3 are 2.0 respectively. 24)15 (-1.21.3] be a set of vectors of a sector space P(1). Show that S be a linearly independent of vectors.
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3.7. Let Br+1 be obtained from Br using the update formula (Yk - BLSK)v" Br+ | Br+1 where v is a vector such that v'sk # 0. Prove that B+1$k = \k•
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(c) A line in R not through the origin ax t by =C #0 then ŏ ¢ H. :. tt s not asubspacd y = 9. Umecersung but ealightenng: X = x You could wnite this as a Sobset, H, of R? H» { ] kek Is H closed under ☺ ? Is H closed under ☺ ļ
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State and Prove the diagonaliy dominent Condition af Convergence of Guass- Jacobi and Gauss - Siedelºmethod. i, e T ail