Question:
If A =
| cos α | -sin α |
| sin α | cos α |
, and A + A’ = I, if the value of α is
If A =
| cos α | -sin α |
| sin α | cos α |
, and A + A’ = I, if the value of α is
Options:
- π
- 3π/2
- π/6
- π/3
- π
- 3π/2
- π/6
- π/3
Correct Answer: d)
Explanation:
Gi√en A = cone B sine
1 sina cosa
‘ Therefore, A’ = cosa one ‘
1 —sina cosa
Also gi√en that A+A’=1…(1)
‘ (Putting the √alues in equation (1))
i cone nal n cosa sine _ B ’
1 sina cosa —sina cosa 01
‘ iN coset cone nat sina _ E
1 sina —sina cosa + cosa 01
2cosa 0 10
‘ = 0 re BN B ’l
We know the two matrices are equal only when all their corresponding elements or entries are
i equal i.e. if A=B, then ajj and bj; for all i and j.
‘ This implies, ‘
2cosa=1
‘ = cosa = 1 i
hon a
‘ = cosa =cosg (cosy =73) ‘
=a=2=Z
3
1 31
‘ (b) 12 ‘
‘
Gi√en A = cone B sine
1 sina cosa
‘ Therefore, A’ = cosa one ‘
1 —sina cosa
Also gi√en that A+A’=1…(1)
‘ (Putting the √alues in equation (1))
i cone nal n cosa sine _ B ’
1 sina cosa —sina cosa 01
‘ iN coset cone nat sina _ E
1 sina —sina cosa + cosa 01
2cosa 0 10
‘ = 0 re BN B ’l
We know the two matrices are equal only when all their corresponding elements or entries are
i equal i.e. if A=B, then ajj and bj; for all i and j.
‘ This implies, ‘
2cosa=1
‘ = cosa = 1 i
hon a
‘ = cosa =cosg (cosy =73) ‘
=a=2=Z
3
1 31
‘ (b) 12 ‘
‘