CBSE Class XII Maths 2016 Question Papers with Solutions

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Question : 1
Total: 26
If A = (
cosαsinα
sinαcosα
)
, find α satisfying 0 < α <
π
2
when A + AT = 2I2 ; where AT is transpose of A.
Solution:  
Consider the given matrix
A = (
cosαsinα
sinαcosα
)
0 < α <
π
2

A + AT = 2I2
(
cosαsinα
sinαcosα
)
+ (
cosαsinα
sinαcosα
)
= 2[
10
01
]

[
2cosα0
02cosα
]
= [
20
02
]

2 cos α = 2
cos α =
2
2
=
1
2

α =
π
4

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