APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 2015
Electronics and Communication Engineering

(Signal Processing)

01 EC6301Applied Linear Algebra ~Max.
Marks : 60 Duration: 3 Hours
PARTA

1 2 3 2
2 _| 4 _[|6 4
_1 ४८ = 1 , 13 = 3
|) Given ul = (3 -2 -[ VI - 111४2

U=span (ய, ५2, ५३) and V—span (VI, v2), Check whether subspace ಟಿಐ subspace V.

(6 Marks)
1 2 1
2) Given vectors ul ‏ول‎ ४2 5-4 ,५३ = -5
2 —1 7
a. Check whether ul, u2 and u3 are linearly independent. (3 Marks)
2 b. Write the vector v= —5 asa linear
combination of given vectors.
3
(3 Marks)

3) a) Given G— {|, 2, 3, 4, 5, 6} under multiplication modulo 7.Find the generator
element(s) ofG. (3 Marks)

1 11
b)Show that the vectorsul = 1, ७2 -, ४३ ‏وت‎ span R? (3 Marks)
1
PART 8
1 3 ‏ا‎
‎4) Given— R* 852 -2 2 Find the matrix 'B' that represents the linear
௦ 1 operator 'A' relative to ; ऽ= the 02555 12. (6 Marks)

¢ 12