घात विधि द्वारा निम्नलिखित आव्यूह का परिमाण में अधिकतम आइगेनमान व संगत आइगेनसदिश ज्ञात कीजिए :$
प्रारम्भिक सन्निकटन (1, 0, 0)T लेकर 4 पुनरावृत्तियाँ कीजिए।
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Construct a field with 125 elements.
Solve the initial value problem using Euler method
Find y(3.1) taking .
Use the Fundamental Theorem of Homomorphism for Groups to prove the following theorem, which is called the Zassenhaus (Butterfly) Lemma:
Let H and K be subgroups of a group G and H' and K' be normal subgroups of H and K, respectively. Then
i)
ii)
iii)
The situation can be represented by the subgroup diagram below, which explains the name ‘butterfly’.
PART-B (MM: 30 Marks)
(Based on Block 3.)
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 velocity of a vehicle beginning from rest is given in the following table for part of the first four. Using Simpson's rule, find the distance travelled by the vehicle in this hour:
|
| 10 | 20 | 30 | 40 | 50 | 60 |
|
| 80 | 60 | 70 | 75 | 70 | 80 |
Is , for any two ideals I and J of a ring R? Give reasons for your answer.
ऑयलर विधि से आदि मान समस्या को हल कीजिए$
लेते हुए y(3.1) ज्ञात कीजिए।