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) = (-x1-1/2x2, 2x1-2x2, 5x2)

the answer is 1/7(3x1-x2, -9x1-4x2, 5x1+10x2)

what did i do wrong here? thanks in advanced