(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive a formula for T.

T([1 1]^T)=[2 -1]^T and

T([1 -1]^T)=[0 3]^T

(...^T=transpose and T(...)=Linear Transformation

2. Relevant equations

T(c1v1+...+cnvn)=c1T(v1)+...+cnT(vn)

3. The attempt at a solution

The solutions manual's method and the method I am supposed to use for these problems.

Let u1=[1 1]^T and u2=[0 -1]^T. If x=[x1 x2]^T then x=[(x1+x2)/2]u1+[(x1-x2)/2]u2...

this is the full solution but I don't know what they are doing here. My question is where did the 1/2's come from?

It says to use the equation that have in the relavant equations part, but I don't see how that would get me where they are.

Using that I would get...

T(u1+u2)=T(u1)+T(u2)=a1u1+a2u2=a1[2 -1]^T + a2[0 3]^T

and I am stuck at this point and don't see a connection between what I have and what they have.

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# Homework Help: Linear transformations

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