The adjoint of the matrix [ beginmatrix cos θ sin θ - sin θ cos θ endmatrix ] is

Question

The adjoint of the matrix [ beginmatrix cos θ sin θ - sin θ cos θ endmatrix ] is (A)  [ beginmatrix cos θ - sin θ sin θ cos θ endmatrix ]  (B)  [ beginmatrix sin θ cos θ cos θ sinθ endmatrix ]  (C)  [ beginmatrix cos θ sinθ -sinθ cos θ endmatrix ]  (D)  [ beginmatrix -sin θ cos θ cos θ sinθ endmatrix ]

Tardigrade Admin · Accepted Answer

Let A=[ beginmatrix cos θ sin θ - sin θ cos θ endmatrix ] Here, C11= cos θ , C12= sin θ C21=- sin θ ,C22= cos θ ∴ adj (A)=[ beginmatrix cos θ sin θ - sin θ cos θ endmatrix ] =[ beginmatrix cos θ - sin θ sin θ cos θ endmatrix ]

Q. The adjoint of the matrix $[cos θ - sin θ sin θ cos θ]$ is

$[cos θ sin θ - sin θ cos θ]$

$[s in θ cos θ cos θ s in θ]$

$[cos θ - s in θ s in θ cos θ]$

$[- s in θ cos θ cos θ s in θ]$

Let $A = [cos θ - sin θ sin θ cos θ]$
Here, $C_{11} = cos θ, C_{12} = sin θ$
$C_{21} = - sin θ, C_{22} = cos θ$
$∴$ adj $(A) = [cos θ - sin θ sin θ cos θ]$
$= [cos θ sin θ - sin θ cos θ]$

Q. The adjoint of the matrix [cosθ−sinθ​sinθcosθ​] is

[cosθsinθ​−sinθcosθ​]

[sinθcosθ​cosθsinθ​]

[cosθ−sinθ​sinθcosθ​]

[−sinθcosθ​cosθsinθ​]