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Byju's Answer
Standard XII
Mathematics
Condition for a Conic to Be a Pair of Straight Lines
The system of...
Question
The system of linear equations:
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4 has a unique solution if
(a) k ≠ 0
(b) −1 < k < 1
(c) −2 < k < 2
(d) k = 0
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Solution
(a) k ≠ 0
For a unique solution,
A
≠ 0.
The given system of equations can be written in matrix form as follows:
1
1
1
2
1
-
1
3
2
k
≠0
⇒
1
k
+
2
-
1
2
k
+
3
+
1
4
-
3
≠0
⇒
k
+
2
-
2
k
-
3
+
1
≠ 0
⇒
k
≠
0
So, the given system of equations has a unique solution if
k
is not equal to 0.
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The system of linear equations:
x + y + z = 2
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3x + 2y + kz = 4 has a unique solution if
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(c) −2 < k < 2
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Condition for a Conic to Be a Pair of Straight Lines
Standard XII Mathematics
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