Thanks for that, but I'm still having some troubles doing this problem. Or I am a little unsure of my answer.
So here's the question.
I attached the image below, because it had all the proper formatting.
So I calculated that
And that the change-of-basis matrix is
And it follows that
The next part is where I am unsure.
So the matrix T with respect to the new basis would just be
but this is just equal to T.
Is that possible?
I did not actually do any computations for this problem (so it is possible that you make a mistake in your computations) but I wanted to say if they are equal then so what? Why is that a problem? If you follow the correct way of getting your computations then your answer would be correct regardless if the new matrix is identical to the old matrix.