Describe fully the transformation Q , represented by the matrix \(\mathbf { Q }\), where \(\mathbf { Q } = \left( \begin{array} { r l } 0 & 1 - 1 & 0 \end{array} \right)\).
The transformation M is represented by the matrix \(\mathbf { M }\), where \(\mathbf { M } = \left( \begin{array} { r r } 0 & - 1 0 & 1 \end{array} \right)\).
M maps all points on the line \(y = 2\) onto a single point, P. Find the coordinates of P.
M maps all points on the plane onto a single line, \(l\). Find the equation of \(l\).
M maps all points on the line \(n\) onto the point ( - 6 , 6). Find the equation of \(n\).
Show that \(\mathbf { M }\) is singular. Relate this to the transformation it represents.
R is the composite transformation M followed by Q . R maps all points on the plane onto the line \(q\). Find the equation of \(q\).