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Mathematics
Problem
Find all value(s) of
k
k
k
for which the system
x
+
2
y
+
3
z
=
4
,
2
x
+
k
y
+
6
z
=
8
,
3
x
+
6
y
+
k
z
=
12
x + 2y + 3z = 4, \\ 2x + ky + 6z = 8, \\ 3x + 6y + kz = 12
x
+
2
y
+
3
z
=
4
,
2
x
+
k
y
+
6
z
=
8
,
3
x
+
6
y
+
k
z
=
12
has infinitely many solutions.
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