Linear Transformation, P2 to R2

[alias]

Homework Statement

T(a+bx+cx^2) = [b+c
a-c]
What is Ker(T)

Homework Equations

I don't the relevant equation(s). I know that the definition of the kernal of a LT is the set of all vectors that are mapped to 0 by T.

The Attempt at a Solution

What I need is a place to start or a hint at a first step.

 

[LCKurtz]

Homework Statement

T(a+bx+cx^2) = [b+c
a-c]
What is Ker(T)

Homework Equations

I don't the relevant equation(s). I know that the definition of the kernal of a LT is the set of all vectors that are mapped to 0 by T.

The Attempt at a Solution

What I need is a place to start or a hint at a first step.

Hint: T(?) = [0,0]

 

[Mark44]

Homework Statement

T(a+bx+cx^2) = [b+c
a-c]
What is Ker(T)

Homework Equations

I don't the relevant equation(s). I know that the definition of the kernal of a LT is the set of all vectors that are mapped to 0 by T.

The Attempt at a Solution

What I need is a place to start or a hint at a first step.

For what values of a, b, and c is the vector <b + c, a - c> equal to the zero vector?

BTW, there is no word "kernal." The one you're looking for is kernel.

 

[alias]

Thanks, I think I understand now.