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Mathematics
Mathematics
Problem
The system of linear equations
x
+
λ
y
−
z
=
0
λ
x
−
y
−
z
=
0
x
+
y
−
λ
z
=
0
\begin{aligned} x + \lambda y - z &= 0 \\ \lambda x - y - z &= 0 \\ x + y - \lambda z &= 0 \end{aligned}
x
+
λ
y
−
z
λ
x
−
y
−
z
x
+
y
−
λ
z
=
0
=
0
=
0
has a non-trivial solution for a. exactly one value of
λ
\lambda
λ
b. exactly two values of
λ
\lambda
λ
c. exactly three values of
λ
\lambda
λ
d. infinitely many values of
λ
\lambda
λ
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