5. (a) \(\mathrm { P } , \mathrm { Q }\) and T are three transformations in 2-D. P is a reflection in the \(x\)-axis. A is the matrix that represents P . Write down the matrix A .
(b)
\(Q\) is a shear in which the \(y\)-axis is invariant and the point \(\binom { 1 } { 0 }\) is transformed to the point \(\binom { 1 } { 2 }\). B is the matrix that represents Q . Find the matrix \(B\).
(c) T is P followed by Q. C is the matrix that represents T. Determine the matrix \(\mathbf { C }\).
(d) \(L\) is the line whose equation is \(y = x\). Explain whether or not \(L\) is a line of invariant points under \(T\).
(e) An object parallelogram, \(M\), is transformed under T to an image parallelogram, \(N\). Explain what the value of the determinant of \(\mathbf { C }\) means about

• the area of \(N\) compared to the area of \(M\),
• the orientation of \(N\) compared to the orientation of \(M\).
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