The shear transformation of \(\RNrSpc{2}\) parallel to the \(x\)-axis with shear vector \(\Vect{s}=(a,0)\) is given by

\[ \FnctnDAAT{S}{\RNrSpc{2}}{\RNrSpc{2}},\quad \FnctnOfTpl{S}{(x,y)} = \left[ \begin{array}{rr} 1 & a \\ 0 & 1 \end{array} \right] \left[ \begin{array}{r} x \\ y \end{array} \right] \]