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Mathematics
Mathematics
Problem
The set of all values of
λ
\lambda
λ
for which the system of linear equations
2
x
1
−
2
x
2
+
x
3
=
λ
x
1
2
x
1
−
3
x
2
+
2
x
3
=
λ
x
2
−
x
1
+
2
x
2
=
λ
x
3
\begin{aligned} 2x_1 - 2x_2 + x_3 &= \lambda x_1 \\ 2x_1 - 3x_2 + 2x_3 &= \lambda x_2 \\ -x_1 + 2x_2 &= \lambda x_3 \end{aligned}
2
x
1
−
2
x
2
+
x
3
2
x
1
−
3
x
2
+
2
x
3
−
x
1
+
2
x
2
=
λ
x
1
=
λ
x
2
=
λ
x
3
has a non-trivial solution a. contains two elements b. contains more than two elements c. is an empty set d. is a singleton
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