No. of Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 2018

Branch: Electrical & Electronics Engineering

(Common to all Streams)

01MA6021: ADVANCED MATHEMATICS AND OPTIMIZATION TECHNIQUES

Answer any twofull questions from each part
Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours
1 2 3 2 ॐ
369 2 3
pace of A=
2 4 6 2 3
1١1 24 8, 3

=(1,1, 1), ‏ولا‎ =(0,1,1) and ‏ولا‎ ಇ(0,

ತ್ತ

PARTA
5 petemnine whether or not ۷ = (2, -5,3) in 8 (4)
श =(1,-3,2), ५, =(2,-4,-1), ‏ولا‎ =(1,-5,7)-in R is a linear combination of the
vectors
0. Find a basis ofthe null space and column space of A= (5)
2; Find an orthonormal basis for R 21011 ப, (4)

6. Find the singular value decomposition of A (5)

3. a. Find the null space and nullity of the linear transformation T:R 3 —+k? defined by (4)
100५2) = (x—y, 0, x+ y).
5 9
1 7
-3 ‏وہ‎ |
0. Find a QR factorization of A 1 5 (5)
PART B
4. Use simplex method to solve the LPP: (9)
Minimize 7 = x, —3x2 +3x3
Subjectto -x2+2x37, +4x2 2-12, -4,q +3x2 +8x3 510, 20.
5. Solve the all integer programming problem by Gomory's cutting plane method: (9)

Maximize 2 = 44 +3X2