Linear Algebra Numerical Analysis - BU 2021 Question Paper

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B.Sc. III^rd Year (Reg./Pvt.) Main Examination, 2021
Mathematics
Paper - I
Linear Algebra & Numerical Analysis

[Maximum Marks: Reg. 40
Pvt. 50]

नाष्ट - प्रत्येक खण्ड से पूछ गये प्रश्शा के अंकस्मान है । प्रत्येक खण्ड का उत्त्ता रनवी न पृष्ठ से प्रारम्भा करे
हल करें । उत्तरपुस्तिका की संख्या 6 सपृम्पठन स्वतःअधि क न हा । विद्याधी द्वारा स्वयं की हस्तलिपिमे उत्तार
है । विद्याथी उत्तरपुस्तिका का प्रथम पृष्ठ विश्वविद्यालक्कीopal कस.क्टस प्राप्त करे ं । ( प्रत्येकप्रसका उ
समान्य 50 शब् दा से अधिक नहा।)

Note :- All questions from each section carry equal marks. All questions are compulsory and answer limit are approximately 250 words. Start the answer of each section from new page. Maximum limit of pages of answer booklet are approximately 16 pages. Answer should be written by the student in his/her own handwriting mandatory. The first page of answersheet should be download by the student from university website is mandatory.

सिद्धकी जिए कि दिन (2, 1, 4), (1, -1, 2) आ (3, 1, -2), V₃(R) का आधारबनाते है।
Prove that the vectors (2, 1, 4), (1, -1, 2) and (3, 1, -2) for a basis of V₃(R).

द्वैत स्मष्टि का उदाहरण सहित परिभाषित की जिए।
Define dual space with example.

यद u, v ∈ V ता सिद्धकरे :
If u, v ∈ V, then prove that:

|(u,v)|≤ ||u||||v||

विभाजित अन्तर से क्य समझते है ?
What do you mean by Divided Differences?

गाँ उ सविला पन विधि का स्पष्ट करें ।
Explain Gauss elimination method.