Question

If $f\left(x\right)=\left[\begin{array}{ccc}cosx& -sinx& 0\\ sinx& cosx& 0\\ 0& 0& 1\end{array}\right]$ then $f(\alpha +\beta )=$

• A. $f\left(\alpha \right)+f\left(\beta \right)$
• B. $f\left(\alpha \right).f\left(\beta \right)$
• C. $f\left(\alpha \right)-f\left(\beta \right)$
• D. $0$

Answer 1

The correct option is B $f\left(\alpha \right).f\left(\beta \right)$

$f\left(\alpha \right).f\left(\beta \right)=\left[\begin{array}{ccc}cos\alpha & -sin\alpha & 0\\ sin\alpha & cos\alpha & 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}cos\beta & -sin\beta & 0\\ sin\beta & cos\beta & 0\\ 0& 0& 1\end{array}\right]=\left[\begin{array}{ccc}cos(\alpha +\beta )& -sin(\alpha +\beta )& 0\\ sin(\alpha +\beta )& cos(\alpha +\beta )& 0\\ 0& 0& 1\end{array}\right]$