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Mathematics
Mathematics
Problem
Consider the system of linear equations:
k
x
+
y
+
z
=
1
k x + y + z = 1
k
x
+
y
+
z
=
1
,
x
+
k
y
+
z
=
1
x + k y + z = 1
x
+
k
y
+
z
=
1
,
x
+
y
+
k
z
=
1
x + y + k z = 1
x
+
y
+
k
z
=
1
. \nFind all real values of
k
k
k
for which this system has a unique solution.
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