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Question
Mathematics
A non-trivial solution of the system of equations x + λ y + 2z = 0, 2x + λ z = 0, 2λ x - 2y + 3z = 0 is given by x: y: z =
Q. A non-trivial solution of the system of equations
x
+
λ
y
+
2
z
=
0
,
2
x
+
λ
z
=
0
,
2
λ
x
−
2
y
+
3
z
=
0
is given by
x
:
y
:
z
=
3678
215
Determinants
Report Error
A
1
:
2
:
−
2
17%
B
1
:
−
2
:
2
17%
C
2
:
1
:
2
46%
D
2
:
1
:
−
2
20%
Solution:
∣
∣
1
2
2
λ
λ
0
−
2
2
λ
3
∣
∣
=
0
⇒
(
2
λ
)
−
λ
(
6
−
2
λ
)
3
+
2
(
−
4
)
=
0
⇒
λ
3
−
2
λ
−
4
=
0
⇒
(
λ
−
2
)
(
λ
2
+
2
λ
+
2
)
=
0
Taking
λ
=
2
, the system becomes
x
+
2
y
+
2
z
=
0
2
x
+
0
y
+
2
z
=
0
4
x
−
2
y
+
3
z
=
0
∴
4
x
=
2
y
=
−
4
z
⇒
x
:
y
:
z
=
2
:
1
:
−
2.