
Linear transformation
Consider the basis S={ v1,v2 } where v1= (2,1), v2=(1,3) and let
T : R^2 > R^3 be the linear transformation such that
T(v1) = ( 1,2,0) and T(v2) = (0,3,5)
Find a formula for T( x1, x2)
Here what I did
let x = (x1,x2) and
c1v1+c2v2=x so
2c1 +1c2 = x1
1c1 + 3c2 = x2 so i have to express c1 and c2 in term of x1 and x2
i get this system
2 1 = x1
1 3 = x2
I use ref(a) to get this
1 1/2 = x1
0 1 = x2
so c2= x2
c1= x1+1/2x2
(x1 +1/2x2)(1,2,0) + (x2)(0,3,5) = (x11/2x2, 2x12x2, 5x2)
the answer is 1/7(3x1x2, 9x14x2, 5x1+10x2)
what did i do wrong here? thanks in advanced

Hey there,
You have the right idea, you just messed up on your algebra. Try redoing your first system of equations.
Working down to RREF I got...
$\displaystyle \begin{bmatrix}1&0\\0&1\end{bmatrix}$ $\displaystyle
=\begin{bmatrix}\frac{x_{2}}{7}\frac{3x_{1}}{7}\\\frac{2x_{2}}{7}+\frac{x_{1}}{7} \end{bmatrix}$
$\displaystyle T(\vec{x_{1}},\vec{x_{2}})=c_{1}(1,2,0)+c_{2}(0,3,5)=$ your books answer!