Chapter 6.5, Problem 54E

To determine

(a)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$

To determine

(b)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$

To determine

(c)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

To determine

(d)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}k& 0\\ 0& 1\end{array}\right]$, $k>1$.

To determine

(e)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}k& 0\\ 0& 1\end{array}\right]$, $0<k<1$.

To determine

(f)

To find:

The transformation defined by the given matrix.

To determine

(g)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}1& 0\\ 0& k\end{array}\right]$, $0<k<1$.

To determine

(h)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}1& k\\ 0& 1\end{array}\right]$

To determine

(i)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{cc}1& 0\\ k& 1\end{array}\right]$

To determine

(j)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \theta & -\sin \theta \\ 0& \sin \theta & \cos \theta \end{array}\right]$

To determine

(k)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{ccc}\cos \theta & 0& \sin \theta \\ 0& 1& 0\\ -\sin \theta & 0& \cos \theta \end{array}\right]$

To determine

(l)

To find:

The transformation defined by the given matrix.

$\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0\\ \sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]$