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AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 5
Total: 160
If A =
[
c
o
s
α
−
s
i
n
α
0
s
i
n
α
c
o
s
α
0
0
0
1
]
, then
(
A
d
j
A
)
−
1
=
A + I
A - I
A
Adj
(
A
−
1
)
3 and 4
Validate
Solution:
Consider the matrix.
A
=
[
cos
α
−
sin
α
0
sin
α
cos
α
0
0
0
1
]
Therefore,
|
A
|
=
cos
2
α
+
sin
2
α
=1
Now,
|
adj A
|
=
|
A
|
3
−
1
=
1
2
=
1
And,
adj(adj A
)
=
|
A
|
3
−
2
⋅
A
=
1
⋅
A
=A
Therefore,
(
a
d
j
A
)
−
1
=
adj(adj A
)
|
adj A
|
=
A
1
=A
© examsnet.com
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