Linear algebra, linear trasformation

[Mdhiggenz]

Homework Statement

let b1=(1,1,0)^T ;b2=(1 0 1)^T; b3=(0 1 1)^T

and let L be the linear transformation from R²

into R³ defined by

L(x)=x₁b₁+x₂b₂+(x₁+x₂)b₃

Find the matrix A representing L with respect to the bases (e₁,e₂)
and (b₁,b₂,b₃)

Homework Equations

The Attempt at a Solution

First thing I did was label out my e1 and e2

e1=(1,0)

e2=(0,1)

L(e1)=b1+b3
= (1,2,1)^T

L(e2)=b2+b3
=(1,1,1)^T

So I would assume my A to be (L(e1),L(e2))^T
However that is incorrect.

I'm not sure what I am doing incorrect the book does the same steps, but gets a different answer.

 

[Fredrik]

Row i, column j of A is $(Le_j)_i$ (i.e. the ith component of $Le_j$ in the given ordered basis). This makes $Le_1$ the first column, but you made it the first row.

Also, you computed $b_2+b_3$ wrong.