# Homework Help: Linear Algebra kernal problem

1. Nov 19, 2007

### mrroboto

1. The problem statement, all variables and given/known data

Let T (element of L(R^2,R^2) ) be the linear map T(a,b) = (a+b, 2a +2b)

A) What is the kernal of T

B) What is the image of T

C) Give the matrix for T in the standard basis for R^2

2. Relevant equations

Kernal of T = {v element of V st T(v) = 0}
Image of T = {w element of W st T(v) = w}

I'm not sure about the matrix

3. The attempt at a solution

I'm really not sure where to go with this. In this case, there are two variable (a,b) instead of 1 variable (v), so I don't know how either the kernal or the image work.

I don't know what standard basis means, and I can't find it in my notes.

Can someone help me?

2. Nov 20, 2007

### FunkyDwarf

Well T is an element of the dual space and it is a map. you want to find the set of points (a,b) such that T(a,b) = (0,0)

As for the image of T try to visualise what the ap is doing to R2

The standard basis is what we normally use as a set of basis vectors, which ill leave you to find out (its pretty obvious youll get it)

3. Nov 20, 2007