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Mathematics
Mathematics
Problem
The sum of distinct values of
λ
\lambda
λ
for which the system of equations
(
λ
−
1
)
x
+
(
3
λ
+
1
)
y
+
2
λ
z
=
0
(\lambda - 1)x + (3\lambda + 1)y + 2\lambda z = 0
(
λ
−
1
)
x
+
(
3
λ
+
1
)
y
+
2
λ
z
=
0
(
λ
−
1
)
x
+
(
4
λ
−
2
)
y
+
(
λ
+
3
)
z
=
0
(\lambda - 1)x + (4\lambda - 2)y + (\lambda + 3)z = 0
(
λ
−
1
)
x
+
(
4
λ
−
2
)
y
+
(
λ
+
3
)
z
=
0
2
x
+
(
3
λ
+
1
)
y
+
3
(
λ
−
1
)
z
=
0
,
2x + (3\lambda + 1)y + 3(\lambda - 1)z = 0,
2
x
+
(
3
λ
+
1
)
y
+
3
(
λ
−
1
)
z
=
0
,
has non-zero solutions, is .
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