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AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper
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© examsnet.com
Question : 4
Total: 160
If A =
[
1
0
0
−
1
]
, P =
[
1
1
0
1
]
and X =
A
P
A
T
then
A
T
X
50
A
=
[
0
1
1
0
]
[
2
1
0
−
1
]
[
25
1
1
−
25
]
[
1
50
0
1
]
Validate
Solution:
Consider the matrix,
A
=
[
1
0
0
−
1
]
since above matrix satisfies
A
A
T
=
I
so, it is an orthogonal matrix then,
A
T
X
50
A
=
A
T
X
49
(
A
P
A
T
)
A
=
A
T
X
49
A
P
(
A
T
A
)
=
A
T
X
49
A
P
=
A
T
X
48
A
P
2
.
.
.
Further simplify the above,
A
T
X
50
A
=
A
T
A
P
50
=
I
P
50
=
P
50
This implies,
P
=
[
1
1
0
1
]
P
2
=
[
1
2
0
1
]
P
3
=
[
1
3
0
1
]
⋮
P
50
=
[
1
50
0
1
]
Therefore, the correct option is (4)
© examsnet.com
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