[2005]
1
Answer-5
2).
Answer-
3
Answer-a,b
[2006]
4
Answer-
5
Answer-
6
Answer-a,b
[2007]
7
Answer-(a)=n (b)=0
8
Answer-a,c
9
Answer-b,c
10
Answer-a,c
11
Answer-a,c
[2008]
12
Answer-0
13
Answer-
14
Answer-0,0,0...... Upto (n-1) times and last eigenvalue is trace of x^ty
15
Answer-a,b,c
16
Answer-
[2009]
17
Answer-a
18
Answer-1
19
Answer-
20
Answer-a,c
[2010]
21
Answer-
22
Answer-a,b
23
Answer-b,c
24
Answer-
[2011]
25
Answer-
26
Answer-
27
Answer-
28
Answer-a,b,c
[2012]
29
Answer-
30
Answer-
31
note-this question is related to above question
Answer-
32
Answer-(a)=n ,(b)=0
33
Answer-a
34
Answer-b,c
[2013]
35
Answer- a-2b-c=0
36
Answer-
37
Note-(this question is realted to above question)
Answer-0
38
Answer-a,b,c
39
Answer-a
40
Note-(this question is related to above question)
Answer-
[2014]
41
Answer-a,b
42
Answer-a,b
43
Answer-a,b,c
44
Answer-a,b
note-(keep in mind on which field he is asking for diagonalizability)
45
Answer-
46
Answer-b,c
47
Answer-
(a)= all the eigenvalues are real and positive
(b)= all the matrices are hermitian so eigen values are real
(c)= all the matrices are skew-hermitian so eigenvalues are zero or purely imaginary
[2015]
48
Answer-
the basis of this space are vectors satisfying the equations x - z + t=0 and 2x + 3y - z + 2t =0
49
Answer- (a)=3 and (b)=1,2
50
Answer-0,0,0...... (n-1) times and n
51
Answer-
52
Answer-
[2016]
53
Answer-(a)=5, (b)=0
54
Answer-
55
Answer-b,c
56
Answer-b
57
Answer-
[2017]
58
Answer-
59
Answer-2,3,4
60
Answer-a
61
Answer-c
62
Answer-
[2018]
63
Answer-
64
Answer-c
65
Answer-b,c
66
Answer-
67
Answer-a,b,c
[2019]
68
Answer-a,b
69
Answer-
and the basis are (1,1,0,1) and (0,0,1,1)
70
Answer-6
71
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