08000MA201122004

a) ⋅ ⋅ dz ⋅ ∙⋅− 7)
Using residue theorem, evaluate ‏مل‎ ಷ್‌ the circle |z-i|=2. (
b) 27 009 (8)
Evaluate S इदः
PART C
Answer any two full questions, each carries 20 marks
a) 1 -1 0 (8)
Find the eigen values and eigen vectors of the matrix}—-1 2 -1.
0 -1 1
0) 1 2 -1 (6)
Find the rank of the matrix | இ 1 0 <
2 4 0
c) Test for consistency and solve the following system (6)
x-y+z=1
2x+y—-—z=2
5x - 2y + 22 = 5.
a) 12 0 1 (8)
Find the basis and dimension of raw space and column space of the matrix}]1 2 1 2
00 1 1
०) Let A= 1 : 1 find AA‘ and A‘A and their traces. (6)
c) Check whether the vectors (1,1,1), (1, -1,1), (1,1, -1) are linearly independent. (6)

a) Write down the matrix associated with the quadratic form 3x2 + 3y?2+2xy=1.Also (8)
convert it to canonical form and find the corresponding transformation.

b) 3 0 0 (12)
Diagonalize the matrix = | -3 4 ‏.او‎
‎0 0 3

मैप ಸೇ

Page 2 of 2