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TS EAMCET 5 May 2018 Shift 2 Solved Paper
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© examsnet.com
Question : 6
Total: 160
If the system
[
2
8
3
7
]
[
a
b
]
=
k
[
a
b
]
has non trivial solution then the positive value of k and a solution of the system for thatvalue of k are
9
,
[
3
8
]
10
,
[
−
8
3
]
6
,
[
−
1
−
1
]
10
,
[
1
1
]
Validate
Solution:
Consider the system of equation.
[
2
8
3
7
]
[
a
b
]
=
k
[
a
b
]
The above equation is solved as,
[
2
a
+
8
b
3
a
+
7
b
]
=
[
k
a
k
b
]
[
a
(
2
−
k
)
+
8
b
3
a
+
(
7
−
k
)
b
]
=
[
0
0
]
[
2
−
k
8
3
7
−
k
]
[
a
b
]
=
[
0
0
]
It has non trivial solution. Therefore,
[
2
−
k
8
3
7
−
k
]
=
0
(
2
−
k
)
(
7
−
k
)
−
24
=
0
k
2
−
9
k
−
10
=
0
(
k
−
10
)
(
k
+
1
)
=
0
since
k
>
0
So,
k
=
10
and
a
=
b
=
1
Therefore, the solutions are 10,10 .
© examsnet.com
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