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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER M.TECH DEGREE EXAMINATION,
DECEMBER 201 7

Electrical & Electronics Engineering

01MA6021: ADVANCED MATHEMATICS AND OVHMIZATION TECHNIQUES
(Common to all streams)

Answer any twofull questions from each part

Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours
PART A(Module 1 and 11)

a. Find the dimension and a basis for the subspace of R* spanned by the vectors (—1, 2,
1), (2, —1, O), and (1, 4, 3)( 4 marks)

b. 101 2
144-95
Find a basis for ColA ; if matrix A =45 —6 (5 marks)
-1 -
2 5

a. Let W be a subspace of R®; prove that its orthogonal complement W 119 a subspace
of IRn. (4 marks)
b. Determine the dimensions of the kernel

and range of the transformation
1. R3 — 1२2 by Z). (5 marks)

a. Find a least square solution of AX b; where
4
A =3 | , =—2 (4 marks)
-3 b. Find the singular value decomposition of

A=2 2 (5 marks)
-1 1

PART B(MOdule 111 & IV)

Using Two Phase Simplex method, solve
Maximize Z = 3xt — X2(9 marks)

Subject (021 + xz 2 2; + 37 5 2 : ५2 4;