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

Suppose A is an mxn matrix and b is a vector in R^m. Define a function T:R^n --> R^m by T(x) = Ax + b. Prove that if T is a linear transformation then b=0.

2. Relevant equations

For the second part of the question, a transformation is linear if:

1) T(u+v) = T(u) + T(v) for all u,v in domain of T

2) T(cu) = cT(u) for all u & c (scalars)

3. The attempt at a solution

For the first part of the question, I am thrown off by the "+b" as I never saw anything other than T(x) = Ax.

However, I am leaning towards using the identity matrix I to prove T(x) = Ax, but I don't feel this will be complete...

I really need a hand getting started and I think I'll be able to pick it up from there.

Thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear transformation arbitrary question

**Physics Forums | Science Articles, Homework Help, Discussion**