- #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...