Chapter 8.8, Problem 6CFU

(a)

To determine

To Find: The transformation matrices.

Answer to Problem 6CFU

The required matrix is $T=\left[\begin{array}{cccccccc}2& 2& 2& 2& 2& 2& 2& 2\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$ .

Explanation of Solution

Given:

The Trevor is revising the design for the play-ground that contains the piece of equipment that is shaped like the rectangular prism.

Trevor needs to enlarge the prism 4 times the size and move it along the x axis 2 units.

Calculation:

Consider the transformation matrix is,

  $M=\left[\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right]$

Multiply the above translational matrix that shifts the prism by 2 units as,

  $T=\left[\begin{array}{cccccccc}2& 2& 2& 2& 2& 2& 2& 2\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

(b)

To determine

To Find: Thegraph of the rectangular prism and the image after the transformation.

Answer to Problem 6CFU

The required graph is shown in Figure 1 and Figure 2

Explanation of Solution

Consider the graph of the rectangular prism is shown in Figure 1

Figure 1

Consider the graph of the image of the rectangular prism is shown in Figure 2

Figure 3