1
$\begingroup$

I'm solving some exercises that I found online relating to transformation matrices and change of basis matrices. I'm having trouble understanding the last part of the answer.

Here's the question:

Let $A = \begin{bmatrix}5&-3\\2&-2\end{bmatrix}$, which is a linear transformation $\mathbb{R}^2 \rightarrow \mathbb{R}^2$. Find the matrix representing the transformation with respect to basis B = $\begin{bmatrix}3&1\\1&2\end{bmatrix}$.

I understand how to solve the question. You would do $B^{-1}AB$. I did the multiplication and got $\begin{bmatrix}20&0\\0&-5\end{bmatrix}$. The author of the document got the same answer but then multiplied the matrix by 1/5 to get $\begin{bmatrix}4&0\\0&-1\end{bmatrix}$. Why is he allowed to do that?

$\endgroup$
2
$\begingroup$

You made a mistake: $1/5$ is included into $B^{-1}$, which you forgot.

$\endgroup$
  • $\begingroup$ You're right! Thanks $\endgroup$ – RakoonBerry Mar 8 at 20:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.