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Mathematics
Mathematics
Problem
The system of linear equations
x
+
λ
y
−
z
=
0
x + \lambda y - z = 0
x
+
λ
y
−
z
=
0
λ
x
−
y
−
z
=
0
\lambda x - y - z = 0
λ
x
−
y
−
z
=
0
x
+
y
−
λ
z
=
0
x + y - \lambda z = 0
x
+
y
−
λ
z
=
0
has a non-trivial solution for : (1) exactly three values of
λ
\lambda
λ
. (2) infinitely many values of
λ
\lambda
λ
. (3) exactly one value of
λ
\lambda
λ
. (4) exactly two values of
λ
\lambda
λ
.
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