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Byju's Answer
Standard XII
Mathematics
Consistency of Linear System of Equations
x + ay = 0, y...
Question
x
+
a
y
=
0
,
y
+
a
z
=
0
,
z
+
a
x
=
0
. The value of a for which the system of equation has infinitely many solutions is
A
a
=
1
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B
a
=
0
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C
a
=
−
1
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D
no value
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Solution
The correct option is
D
a
=
−
1
△
=
0
⇒
∣
∣ ∣
∣
1
a
0
0
1
a
a
0
1
∣
∣ ∣
∣
=
0
o
r
1
+
a
3
=
0
or
(
1
+
a
)
(
1
−
a
+
a
2
)
=
0
∴
a
=
−
1
.
The other factor does not give real value of a.
Suggest Corrections
0
Similar questions
Q.
If the system of equations x + ay = 0, az + y = 0, ax + z = 0 has infinitely many solutions then a = ___________________.
Q.
The real value of 'a' for which the equations ax+y+z=0, -x+ay+z=0, -x-y+az =0 have nonzero solution is
Q.
Consider the system of equations:
x
+
a
y
=
0
,
y
+
a
z
=
0
and
z
+
a
x
=
0
. Then the set of all real values of
′
a
′
for which the system has a unique solution is
Q.
If the system of equations
x
+
a
y
=
0
,
a
z
+
y
=
0
,
a
x
+
z
=
0
has
infinite number of solutions then the value of
a
is
Q.
Assertion :If a, b, c
ϵ
R
and
a
≠
b
≠
c
and x, y, z are non zero. Then the system of equations
a
x
+
b
y
+
c
z
=
0
b
x
+
c
y
+
a
z
=
0
c
x
+
a
y
+
b
z
=
0
has infinite solutions. Reason: If the homogeneous system of equations has non trivial solution, then it has infinitely many solutions.
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