APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER M.TECH DEGREE EXAMINATION
DECEMBER 2015
Electrical and Electronics Engineering
(COMMON to all streams)
01MA6021: Advanced Mathematics & Optimization Techniques ~
Time: 3 hours Max: Marks : 60

Answer any two full questions from each part.

PART-A (Module: and 11)

1. aDetermine whether ऽ 7 ‏و5 ہج‎ ) 2:20, Xie २ 215 8 subspace of R * . Justify

your answer. (4)

< رو 4- 1
1 = 2 1=

b.Find a basis for the null space and column space of A = 5 -6 10 7! [

2. a.Let T be defined by T (x, ೫) = ex + ೫, 5x+ 7y,X+3y). Show that T is a one to one

linear transformation. Does T map २८ onto R 3 (4)
b. Let U be the sub space of R? spanned by the vectors ur = --5 and =—I
Find an orthonormal basis for U by Gram-Schmidt orthogonalization process . {5)
1 0 2
3. कसित a singular value decomposition of A = (2. 1, 0 {5)
40
b. Find a least squares solution of the inconsistent system Ax = b where A = O 2 and
(4)
11
PART-B (Module 11 and IV)
4. a.Solve the following LPP by simplex method. Minimize f = —x, — 2x2 — , subject to the
constraints 2201 + X2 —X, ऽ 3, 2X] —xa+5X3 ऽ 6, 4X1 + X2 +X, 6,
x, , 22, 3 2 0 (6)
b. Construct the dual of the LPP
Maximize f = + IOOX2 subject to the constraint 2x, + x2 5 1250,

2% 4512S 1000, +3X2 000, ೫2 < 150, ೬೬೫೨2 20 (3)