1. ## Linear Transformation

Hi There,

Just need some help with this question, would really appreciate your help,

Let u1 = (1,2,1), u2 = (0,1,1) and u3=(1,1,1)
Also let v1 = (1,2,3,4) v2 = (1,0,1,0) and v3 = (2,1,0,3)

Find a Matrix A such that Ta(uk)= vk for all 1<=k<=3

Have an exam coming up and I'm stumped on this

2. Originally Posted by Ben85
Hi There,

Just need some help with this question, would really appreciate your help,

Let u1 = (1,2,1), u2 = (0,1,1) and u3=(1,1,1)
Also let v1 = (1,2,3,4) v2 = (1,0,1,0) and v3 = (2,1,0,3)

Find a Matrix A such that Ta(uk)= vk for all 1<=k<=3

Have an exam coming up and I'm stumped on this
The first thing you need to do is find a way of expressing this transformation. Express v1 given u1, v2 given u2 and v3 given u3. From there you can construct the matrix that you want, which will satisfy T(u)=Au=v.

Matrix A times the column vector [u1,u2,u3] will equal [v1,v2,v3,v4] (imagine those are columns). So A must be a 4x3 matrix and will be multiplied by the 3x1 column matrix for u, resulting in a 4x1 column matrix representing v. Each row in A will [a1,a2,a3] such that a1u1+a2u2+a3u3=v1.