Let a = matrix cosx-isinx 0
0 cosx-isinx
Find the value of x for which (as bar
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Class 12
>>Maths
>>Matrices
>>Transpose of a Matrix
>>If A = , then find x satis...
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If A=[
cosx
−sinx
sinx
cosx
], then find x satisfying 0<x<
2
π
when A+A
T
=I.
Medium
Solution
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A=[
cosx
−sinx
sinx
cosx
]
⇒ A
T
=[
cosx
sinx
−sinx
cosx
]
Now,
A+A
T
=I
⇒ [
cosx
−sinx
sinx
cosx
] +[
cosx
sinx
−sinx
cosx
] =[
1
0
0
1
]
⇒ [
cosx+cosx
−sinx+sinx
sinx−sinx
cosx+cosx
]=[
1
0
0
1
]
⇒ [
2cosx
0
0
2cosx
]=[
1
0
0
1
]
⇒ 2cosx=1
⇒ cosx=
2
1
⇒ x=
3
π
∴ We can see x satisfied the condition 0<x<
2
π
.
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