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Question
Mathematics
If the trivial solution is the only solution of the system of equations x - ky + z = 0 kx + 3y - kz = 0 3x +y - z = 0 then the set of all values of k is :
Q. If the trivial solution is the only solution of the system of equations
x
−
k
y
+
z
=
0
k
x
+
3
y
−
k
z
=
0
3
x
+
y
−
z
=
0
then the set of all values of k is :
2414
221
Determinants
Report Error
A
R -{2,-3}
58%
B
R -{2}
17%
C
R -{-3}
25%
D
{2,-3}
0%
Solution:
x
−
k
y
+
z
=
0
k
x
+
3
y
−
k
z
=
0
3
x
+
y
−
z
=
0
The given system of equations will have non trivial solution, if
∣
∣
1
k
3
−
k
3
1
1
−
k
−
1
∣
∣
=
0
⇒
1
(
−
3
+
k
)
+
k
(
−
k
+
3
k
)
+
1
(
k
−
9
)
=
0
⇒
k
−
3
+
2
k
2
+
k
−
9
=
0
⇒
k
2
+
k
−
6
=
0
⇒
k
=
−
3
,
k
=
2
So the equation will have only trivial solution,
when
k
∈
R
−
{
2
,
−
3
}