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Byju's Answer
Standard XII
Mathematics
Cramer's Rule
The equations...
Question
The equations
λ
x
−
y
=
2
,
2
x
−
3
y
=
−
λ
,
3
x
−
2
y
=
−
1
are consistent for
A
λ
=
−
4
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B
λ
=
−
1
,
4
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C
λ
=
−
1
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D
λ
=
1
,
−
4
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Solution
The correct option is
B
λ
=
−
1
,
4
∣
∣ ∣
∣
λ
−
1
−
2
2
−
3
λ
3
−
2
1
∣
∣ ∣
∣
=
0
⇒
λ
(
−
3
+
2
λ
)
+
1
(
2
−
3
λ
)
−
2
(
−
4
+
9
)
=
0
⇒
2
λ
2
−
6
λ
−
8
=
0
⇒
λ
2
−
3
λ
−
4
=
0
⇒
(
λ
−
4
)
(
λ
+
1
)
=
0
∴
λ
=
−
1
,
4
Suggest Corrections
0
Similar questions
Q.
The equations
λ
x
−
y
=
2
,
2
x
−
3
y
=
−
λ
,
3
x
−
2
y
=
−
1
are consistent for
Q.
Determine the value of
λ
for which the following system of equations fail to have a unique solution.
λ
x
+
3
y
−
z
=
1
x
+
2
y
+
z
=
2
−
λ
x
+
y
+
2
z
=
−
1
Does it have any solution for
λ
=
1
?
Q.
Find the value of
λ
for which the set of equations
x
+
y
−
2
z
=
0
,
2
x
−
3
y
+
z
=
0
,
x
−
5
y
+
4
z
=
λ
are consistent.
Q.
If the system of equations
x
+
2
y
−
3
=
0
2
x
−
y
+
4
=
0
λ
x
+
y
−
3
=
0
are consistent then the value of
λ
is
Q.
Find the value of
λ
, if the following equations are consistent
x
+
y
−
3
=
0
(
1
+
λ
)
x
+
(
2
+
λ
)
y
−
8
=
0
x
−
(
1
+
λ
)
y
+
(
2
+
λ
)
=
0
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