Vinayaka Missions University 2008 B.Sc Mathematics LINEAR ALGEBRA : T : CORRESPONDENCE - Question Paper

COURSE CODE – 1030503
UG DEGREE exam – SEP 2008
BSC (MATHS)
LINEAR ALGEBRA
(For Candidate Admitted from Calendar 2007 Onwards)
Time: three Hours Max. Marks: 75
part - A
ans all the questions:- 15 X 1=15
1. describe power series
2. provide an example for exponential series
3. describe logarithmic series
4. State any five prime numbers
5. State Decomposition theorem
6. describe Euler function.
7. provide an example for 2nd degree polynomial
8. What is the rate of convergent in Newton’s method
9. What is reciprocal equations?
10. describe hermitian matrix.
11. What is symmetric matrix. provide an example for it.
12. obtain the rank of the subsequent matrix.
2 three 5
6 seven 8
6 five 4
? ?
? ?
? ?
? ?
? ?
13. State cayley Hamilton theorem.
14. describe characteristic root of a matrix.
15. describe Eigen values.
part – B
ans any 5 questions: five X six = 30
16. a) Sole Z = P X + qy + p2 – q2
(or)
b) Eliminate ‘f’ from Z = f (X2 + Y2 + 22 )
17. a) Prove that (a +b)n = nc
o ao bn-o + nc
1 a1 bn-1+ ……
(or)
b) Derive the formula for Fourier constants for f(?) in (- p, p).
18. a) obtain the roots of the subsequent formula by Newton’s
method.
F(?) = ?2 + two ? +5
(Or)
b) obtain the root of the subsequent formula by Horner’s method
F (?) = ?2 + two ? + CoS ? +7
19. a) obtain Eigen value of A where A=
1 four 4
1 two 4
2 one 3
? - ?
? ?
? - ?
?? - ??
(Or)
b) obtain inverse of a matrix a where A =
6 two 3
5 four 3
6 eight 7
? ?
? ?
? ?
? ?
? ?
20. a) decrease the subsequent symmetrix matrix A to the diagonal
form and interpret the outcome in terms of Quadratic forms
12 three 3
3 four 2
3 two 5
? - ?
? ?
?- - ?
?? - ??
(Or)
b) obtain triangular reduction of a positive definite matrix
part – C
ans any 2 questions: two X 15 = 30
21. discuss singular value decomposition with an example.
22. State and prove WILSON’S theorem and congruence’s
theorem.
23. Write short note on
a. Irrational roots
b. Complex roots
c. New ton’s method
d. Horner’s method.
24. By reducing the quadratic form
3 ?1
2 - three ?2
2 - three ? 3
2 - 5? 3
2 -2?1 ? 2
- six ?2 ? three - six ?3 ?1 to
Canonical form, determine its rank, index and signature.
25. Using Cayley- Hamilton theorem, obtain Inverse of the matrix.
1 0 3
8 one 7
3 0 8
? - ?
? ?
? - ?
??- ??

Earning:   Approval pending.