Find the eigenvalues and eigenvectors of matrix A=
1.
42
11
−
⎡⎤
⎢⎥
⎣⎦
.
Ans: 2, 3;
12
12
,
11
XX
⎡⎤ ⎡⎤
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
2.
14
15
⎡⎤
⎢⎥
⎣⎦
.
Ans:
1, 6;
12
41
,
11
XX
−
⎡⎤⎡⎤
⎢⎥⎢⎥
⎣⎦⎣⎦
3.
432
23
1
213
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
−
⎣⎦
. [JNTU 2003 (1) 2005 S(3)]
Ans:
2, 2, 8;
3
12
112
0, 2 1
201
X
XX
⎡⎤⎡⎤⎡
⎤
⎢⎥⎢⎥⎢
⎥
−
⎢⎥⎢⎥⎢
⎥
⎢⎥⎢⎥⎢
⎥
−
⎣⎦⎣⎦⎣
⎦
4.
201
020
102
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
. [JNTU 2000 S]
Ans:
1, 2, 3;
3
12
110
0, 0 1
110
X
XX
⎡⎤⎡⎤⎡⎤
⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥
⎢⎥
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