If I=[1&0 0&1], J=[0&1 -1&0] and B=[cos θ&sin θ - sin θ cos θ ], then B is equal to

Question

If I=[1&0 0&1], J=[0&1 -1&0] and B=[cos θ&sin θ - sin θ cos θ ], then B is equal to (A) I cos θ+J sin θ  (B) I sin θ+J cos θ  (C) I cos θ-J sin θ  (D) -I cos θ+J sin θ

Tardigrade Admin · Accepted Answer

B=[ cos θ sin θ - sin θ cos θ] =[ cos θ 0 0 cos θ]+[0 sin θ - sin θ 0] = cos θ[1 0 0 1]+ sin θ[0 1 -1 0] =I cos θ+J sin θ

Q. If $I = [1001], J = [0 - 1 10]$ and $B = [cos θ - sin θ s in θ cos θ],$ then $B$ is equal to

$I cos θ + J sin θ$

$I sin θ + J cos θ$

$I cos θ - J sin θ$

$- I cos θ + J sin θ$

$B = [cos θ - sin θ sin θ cos θ]$
$= [cos θ 0 0 cos θ] + [0 - sin θ sin θ 0]$
$= cos θ [1001] + sin θ [0 - 1 10]$
$= I cos θ + J sin θ$

Q. If I=[10​01​],J=[0−1​10​] and B=[cosθ−sinθ​sinθcosθ​], then B is equal to

Icosθ+Jsinθ

Isinθ+Jcosθ

Icosθ−Jsinθ

−Icosθ+Jsinθ