3005
You visited us
3005
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Solving Simultaneous Linear Equation Using Cramer's Rule
Let λ and ...
Question
Let
λ
and
α
be real. The set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
−
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
has a non-trivial solution is
A
[
0
,
√
2
]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[
−
√
2
,
0
]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[
−
√
2
,
√
2
]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
D
[
−
√
2
,
√
2
]
Since the system has a non-trivial solution, therefore
∣
∣ ∣
∣
λ
sin
α
cos
α
1
cos
α
sin
α
−
1
sin
α
−
cos
α
∣
∣ ∣
∣
=
0
⇒
λ
(
−
cos
2
α
−
sin
2
α
)
−
(
−
sin
α
cos
α
−
sin
α
cos
α
)
−
(
sin
2
α
−
cos
2
α
)
=
0
⇒
−
λ
+
sin
2
α
+
cos
2
α
=
0
⇒
λ
=
sin
2
α
+
cos
2
α
⇒
λ
=
√
2
cos
(
2
α
−
π
4
)
≤
1
∀
α
∈
R
∴
−
√
2
≤
λ
≤
√
2
⇒
λ
∈
[
−
√
2
,
√
2
]
Suggest Corrections
1
Similar questions
Q.
Let
λ
and
α
be real. Let
S
denote the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
has a non-trivial solution then
S
contains
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equation
λ
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
x
+
(
c
o
s
α
)
y
+
(
s
i
n
α
)
z
=
0
−
x
+
(
s
i
n
α
)
y
−
(
c
o
s
α
)
z
=
0
has a non-trivial solution. For
λ
=
1
, find all values of
α
Q.
Let S denote the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
,
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
,
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
,
has a non-trivial solution
∀
α
∈
R
, then S contains
Q.
The system of equation
(
sin
α
)
x
+
2
z
=
0
,
(
cos
α
)
x
+
(
sin
α
)
y
=
0
;
(
cos
α
)
y
+
2
z
=
a
has (where a and
α
are constants)
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equations
λ
x
+
(
sin
α
)
y
+
(
cos
α
)
z
=
0
,
x
+
(
cos
α
)
y
+
(
sin
α
)
z
=
0
and
−
x
+
(
sin
α
)
y
−
(
cos
α
)
z
=
0
Has a non-trivial solution. For
λ
=
1
, find all values of
α
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Cramer's Rule
MATHEMATICS
Watch in App
Explore more
Solving Simultaneous Linear Equation Using Cramer's Rule
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app