The discussion revolves around finding the kernel of a linear transformation defined by T(a+bx+cx^2) = [b+c, a-c]. Participants are exploring the concept of the kernel in the context of linear transformations from P2 to R2.
Some participants have expressed a need for guidance on how to begin solving the problem, while others have provided hints to consider the equation T(?) = [0,0] as a starting point. There is an acknowledgment of a terminology issue regarding the term "kernal," which has been corrected to "kernel."
Participants note a lack of relevant equations and express uncertainty about the initial steps needed to approach the problem.
alias said: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?alias said: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.