Chapter 6.3, Problem 79PE

a. Write a matrix A that represents the coordinates of the vertices of the triangle. Place the x -coordinate of each point in the first row of A and the corresponding y -coordinate in the second row of A. (See Example 9)

b. Use addition of matrices to shift the triangle 2 units to the right and 4 units downward.

c. Find the product $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]\cdot A$ and explain the effect on the graph of the triangle.

d. Find the product $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\cdot A$ and explain the effect on the graph of the triangle.

e. Find $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\cdot A+\left[\begin{array}{ccc}-1& -1& -1\\ 2& 2& 2\end{array}\right]$ and explain the effect on the graph of the triangle.