Recent content by patricio2626

I think that if I can get an answer to this then I will be able to figure out what is going on in the answer and explanation in the book: I'm confused at what exactly a transform matrix relative to a given basis is to mean. Does this mean that some vector vB', when multiplied by A', will equal...

Sure, T(e1), T(e2) is easy: {(2, -1), (0, 2)}

'Homework Statement Find the matrix A' for T: R2-->R2, where T(x1, x2) = (2x1 - 2x2, -x1 + 3x2), relative to the basis B' {(1, 0), (1, 1)}. Homework Equations B' = {(1, 0), (1, 0)} so B'-1 = {(1, -1), (0, 1)}. The Attempt at a Solution I'm confused at what exactly a transform matrix...

Thanks gents, this got me past this headscratcher, and then I had an on-the-fly tutor session yesterday and I get it now. To convert between nonstandard bases and find a transform for a vector expressed in the standard basis: -To get the relative matrix we transform the first nonstandard base...

Okay, so v = (2, 1) = 1(1, 2) - 1(-1, 1) because 1*1 - 1*-1 = 2 1*2 - 1*1 = 1 So, the book simply skipped this piece of the explanation?

Homework Statement For the linear transformation T: R2-->R2 defined by T(x1, X2) = (x1 + x2, 2x1 - x2), use the matrix A to find T(v), where v = (2, 1). B = {(1, 2), (-1, 1)} and B' = {(1, 0), (0, 1)}.Homework Equations T(v) is given, (x1+x2, 2x1-x2) The Attempt at a Solution Okay, I see...