No: of pages: 2
AP.J ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER M, TECH DEGREE EXAMINATION, DECEMBER 2017
Electronics and Communication Engineering
1.Signal Processing
2. Telecommunication Engineering
01 EC6301 Applied Linear Algebra

Max. Marks : 60 Duration: 3 Hours

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

I a) Prove that the identity element of a group G is unique and the inverse of each
element ofG is unique. (4 marks)

b) Solve by Gauss Elimination method
2x + ) + 22 + ॥# = 6, ಜ-೫ 2 + 2w = 6,
4x +3y + 32 - 3# = -1, 2x + 2/- 2 + \# = 10 (5 marks)

2 a)Define subspace of a vector space. Prove that the intcrsection oftwo subspaces
of a vector space is a subspace. (4 marks)

b) Find a spanning set for the Null space of, where
-3 6 -1 | 7
4= | 1 -2 2 3 |

2-4 5 8 -4[- 1 (5 marks)

3 a) Prove that a subset ऽ of a vector space V is a basis of ۷ if and only if Sis a
minimal generating set. (4 marks)

1 -2
பு] 2
10 3
ए) Find theleast square solution of the system AX =BwhereA (2 5 Jand
3
_ | |
|-4

2 JAlso compute the least square error. (5 marks)