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AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 4
Total: 160
The sum of the values of x so that the matrix
(
2
2
1
1
3
1
1
2
2
)
- x
(
1
0
0
0
1
0
0
0
1
)
is singular, is
3
5
7
9
Validate
Solution:
Consider the matrix,
(
2
2
1
1
3
1
1
2
2
)
−
x
(
1
0
0
0
1
0
0
0
1
)
It is solved as,
(
2
2
1
1
3
1
1
2
2
)
−
x
(
1
0
0
0
1
0
0
0
1
)
=
[
2
−
x
2
1
1
3
−
x
1
1
2
2
−
x
]
The matrix is singular. Therefore,
|
2
−
x
2
1
1
3
−
x
1
1
2
2
−
x
|
=
0
Apply operation
C
1
→
C
1
+
C
2
+
C
3
|
5
−
x
2
1
5
−
x
3
−
x
1
5
−
x
2
2
−
x
|
=
0
(
5
−
x
)
|
1
2
1
1
3
−
x
1
1
2
2
−
x
|
=
0
Apply operation
R
2
→
R
2
−
R
1
and
R
3
→
R
3
−
R
1
(
5
−
x
)
|
1
2
1
0
1
−
x
0
0
0
1
−
x
|
=
0
(
5
−
x
)
(
1
−
x
)
2
=
0
x
=
1
,
5
,
5
Thus, the sum of the required value of x is,
Sum= 1 + 1 + 5 = 7
© examsnet.com
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