Chapter 11.FOM, Problem 6P

Here is a data matrix for a line drawing:

$D=\left[\begin{array}{cccccc}0& 1& 2& 1& 0& 0\\ 0& 0& 2& 4& 4& 0\end{array}\right]$

(a) Draw the image represented by $D$.

(b) Let $T=\left[\begin{array}{cc}1& 1\\ 0& -1\end{array}\right]$. Calculate the matrix product $TD$, and draw the image represented by this product. What is the effect of the transformation $T$?

(c) Express $T$ as a product of a shear matrix and a reflection matrix. (See Problem 2.)

$2.$ Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use $c=3$ in the expansion matrix and $c=1$ in the shear matrix.

$T_1=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$ Reflection in $y-\text{axis}$

$T_2=\left[\begin{array}{cc}1& 0\\ 0& c\end{array}\right]$ Expansion (or contraction) in $y-\text{direction}$

$T_3=\left[\begin{array}{cc}1& 0\\ c& 1\end{array}\right]$ Shear in $y-\text{direction}$