If , find the values of C1 and C2.
Given the finite difference approximation for the second difference: [ \delta^2 f(x_0) = C_1 h^2 f''(x_0) + C_2 h^4 f^{(4)}(x_0) + \cdots ] We want to find constants (C_1) and (C_2). --- Start with the definition of the second _______ _______ _______ _____ _______ ____.
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Prove that every non-trivial subgroup of a cyclic group has finite index. Hence prove that is not cyclic.
Let G be an infinite group such that for any non-trivial subgroup H of . Then prove that
i) or H is infinite;
ii) If , then o(g) is infinite.
The Gauss-Seidel method is used to solve the system of equations
Determine the rate of convergence of the method.
Which of the following statements are true? Give reasons for your answers.
i) If a group G is isomorphic to one of its proper subgroups, then .
ii) If x and y are elements of a non-abelian group (G, ) such that , then
or
, where e is the identity of G with respect to $$.
iii) There exists a unique non-abelian group of prime order.
iv) If , where A is a group, then
.
v) If H and K are normal subgroups of a group G, then .
Prove that a cyclic group with only one generator can have at most 2 elements.
विधि$
जहाँ N एक धन अचर है, N1/3 की ओर अभिसरित होती है। विधि की अभिसरण दर ज्ञात कीजिए।
निम्नलिखित समीकरण निकाय को हल करने के लिए गाउस–सीडल पुनरावृत्ति विधि को आव्यूह रूप में स्थापित कीजिए :
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दिखाइए कि पुनरावृत्ति विधि अभिसरित होती है और अतः इसकी अभिसरण दर ज्ञात कीजिए। (5)