Some Matrices and Parallelograms

In this problem we'll want to consider the vectors:

$${\bf v1} = \left( \begin{array}{r} 1 \\ 0 \end{array} \right... ...{\bf v5} = \left( \begin{array}{r} 1 \\ 1 \end{array} \right),$$

and

$${\bf v6} = \left( \begin{array}{r} -1 \\ 1 \end{array} \right)$$

We will also consider the parallelograms:

• P1 with edges ${\bf v1}$ and ${\bf v2}$.
• P2 with edges ${\bf v3}$ and ${\bf v4}$.
• P3 with edges ${\bf v5}$ and ${\bf v6}$.
• P4 with edges ${\bf v1}$ and ${\bf v6}$.

And the matrices

$${\bf A1} = \left(\begin{array}{rr} .28 & .96 \\ .96 & -.28 \... ... = \left(\begin{array}{rr} 2 & -1 \\ 1 & 0 \end{array}\right),$$

as well as

$${\bf A4} = \left(\begin{array}{rr} .04 & .72 \\ -1.28 & 1.96... ... = \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right),$$

and

$${\bf A7} = \left(\begin{array}{rr} 1 & 2 \\ 2 & 4 \end{array}\right),$$

It is probably a good idea to start out by entering these vectors and matrices in your Maple session. The file :Maple V Release 4:Math 221:Spring 98 #2 vectors and matrices contains these already typed in. Remember you have to actually execute the lines in your current session for the assignments to take effect.