Hi!

i have a doubt here:

Excercise:

Given:

Both are basis from the V linear space.

and

-->Find

So, my plan was:

Get the change of basis matrix, this is easy because of the way the basis are expresed

Seems like you go by columns; fine, it's just the same...as long as you keep it being constant. Anyway, the second column's first entry (the matrix's 12 entry) must be 1, not zero.[/color]

Now i know that \left(\begin{array}{ccc}1&-2&1\\2&6&-6\\1&3&-3\end{array}\right)" alt="

\left(\begin{array}{ccc}1&-2&1\\2&6&-6\\1&3&-3\end{array}\right)" />

Now i just do And those columns are the image of but expresed in , so, image well expresed is butīs LD, so ----------------------------------------- So, the problem is that in the book i found a proposition that says that given linear functions and ----------------------------------------------------- So, that, what i have done is:
[color=red]

This is all you need: this is the correct answer. Tonio
and i know now that the image of the LT are the colums of the matrix, but those are expresed in

so, the image is going to be formed by:

butīs LD, so

Unfortunately, both results are different!!

which is the correct one? where is the mistake?