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AP EAMCET Engineering 2013 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 83
Total: 160
If
I
is the identity matrix of order 2 and
A
=
[
1
1
0
1
]
, then for
n
≥
1
, mathematical induction gives
A
n
=
n
A
−
(
n
−
1
)
I
A
n
=
n
A
+
(
n
−
1
)
I
A
n
=
2
n
A
−
(
n
+
1
)
I
A
n
=
2
n
−
1
A
−
(
n
−
1
)
I
Validate
Solution:
Given
A
=
[
1
1
0
1
]
A
2
=
[
1
1
0
1
]
[
1
1
0
1
]
=
[
1
+
0
1
+
1
0
+
0
0
+
1
]
=
[
1
2
0
1
]
Similarly,
A
3
=
[
1
3
0
1
]
A
n
=
[
1
n
0
1
]
We have,
n
A
−
(
n
−
1
)
I
=
[
n
n
0
n
]
−
[
n
−
1
0
0
n
−
1
]
=
[
1
n
0
1
]
=
A
n
A
n
=
n
A
−
(
n
−
1
)
I
is true
© examsnet.com
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