I'm now solving an exercise, in which I have to calculate the image array of all 2x2 matrices on their transposed with the standard basis B.
$$B= \begin{pmatrix}1&0\\ 0& 0\end{pmatrix}$$ \begin{pmatrix}0&1\\ 0& 0\end{pmatrix}$$ \begin{pmatrix}0&0\\ 1& 0\end{pmatrix}$$ \begin{pmatrix}0&0\\ 0& 1\end{pmatrix}
As fas as I understood, I've to calculate the image array of:
\begin{pmatrix}a11&a12\\ a21& a22\end{pmatrix}
to:
\begin{pmatrix}a11&a21\\ a12& a22\end{pmatrix}
But how do I do that?
I hope someone can help me!!!
Greetings and a very nice Friday evening!!!