- #1

ehrenfest

- 2,020

- 1

## Homework Statement

1) Show that for any real numbers a and b, the matrices

[tex] \left( \begin{array}{cc}

1 & a \\

0 & 2 \\

\end{array}\right)[/tex]

and

[tex] \left(\begin{array}{cc}

1 & b \\

0 & 2 \\

\end{array}\right)[/tex]

are similar.

2) Show that

[tex] \left( \begin{array}{cc}

2 & 1 \\

0 & 2 \\

\end{array}\right)[/tex]

and

[tex] \left(\begin{array}{cc}

2 & 0 \\

0 & 2 \\

\end{array}\right)[/tex]

are not similar.

## Homework Equations

## The Attempt at a Solution

We want to show that B=P^{-1} A P holds for some P in the first case and holds for no P in the second case. So I let P be an arbitrary 2 by 2 matrix and just wrote out the four equations that you get using the explicit formula for the inverse but that failed . So what is the trick...