I wish to compute the change of basis for the following:

B = {

}

C = {

}

How can I compute the change of basis matrix

?

There are supposedly (at least) two ways to do this.

I know how to do this by expressing the vectors in B in terms of the basis C; when I do that I get the result that:

=

Is this correct at all? Although even if it is correct I'd like to be able to do it using a different approach I got described.

It is correct and hopefully you understand what you did here: you express each element of the new

basis as a lin. combination of the new basis and the matrix we're looking for is the transpose of the

coefficient matrix obtained in the first step.

This is, as far as I can tell, the easiest and quickest method.
Supposedly I first have to transform the B coordinates to the canonical coordinates and thereafter the canonical coordinates to C coordinates, this should give

as

Could someone show me how to do this for this example?