$\mathrm{A}\left[\begin{array}{ccc}1& 0& 0\\ -\tan & 1& 0\\ 0& 0& 1\end{array}\right]=\left[\begin{array}{ccc}\mathrm{cos\theta }& -\mathrm{sin\theta }& 0\\ 0& {\displaystyle \frac{1}{\mathrm{cos\theta }}}& 0\\ 0& 0& 1\end{array}\right]$

R₂ → R₂cosθ 
$\mathrm{A}\mid \begin{array}{ccc}1& 0& 0\\ -\mathrm{sin\theta }& \mathrm{cos\theta }& 0\\ 0& 0& 1\end{array}\mid =\mid \begin{array}{ccc}\mathrm{cos\theta }& -\mathrm{sin\theta }& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\mid$
R₁ → R₁ + sinθR₂

 $\mathrm{A}\mid \begin{array}{ccc}1-\sin & \mathrm{sin\theta }& 0\\ -\mathrm{sin\theta }& \mathrm{cos\theta }& 0\\ 0& 0& 1\end{array}\mid =\mid \begin{array}{ccc}\mathrm{cos\theta }& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\mid$

R₁ → R₁ / cosθ

$\mathrm{A}\mid \begin{array}{ccc}\mathrm{cos\theta }& \mathrm{sin\theta }& 0\\ -\mathrm{sin\theta }& \mathrm{cos\theta }& 0\\ 0& 0& 1\end{array}\mid =\mid \begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\mid$