What Are the Kernel and Image of the Linear Map T?

[mrroboto]

Homework Statement

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

Homework 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

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?

 

[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)

 

[catscradle]

The key for the standard basis is R^2. It's different for all R^n, so focus on the two