Calculation of Im A of all Matrices 2x2 on it's transposed

32 Views Asked by At

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!!!