Originally Posted by

**HallsofIvy** But to generalize: If L is a linear transformation from vector space U, with dimension n, to vector space V, with dimension m, then it can be written in matrix form for given basis

of U and given basis

of V (changing bases will result in different but "equivalent" matrices representing the same transformation).

Take

and write it as a linear combination of the basis

, which you can do since

is in V. Say,

. Then

is the first column in the matrix. Similarly, writing

as a linear combination of

gives the second column, etc.

I'm new to a lot of this stuff so some of that definition didn't really make sense to me... You are saying that i would have to approach a problem like the one below differently, correct?

(b) Let

L : R3 ->R2 be the linear transformation defined by

L

(x, y, z) = (x + y + z, y + z)

(i) Find the standard (2 × 3) matrix representation of L and compute L(0,−1, 1).