# Homework Help: Kernel of a Transformation that is a differential equation

1. May 4, 2012

### FHamster

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

Calculate the kernel of https://webwork3.math.ucsb.edu/webwork2_files/tmp/equations/f7/04b646ac1797cdf54f4a373ce5ef431.png [Broken]
Since T is a linear transformation on a vector space of functions, your kernel will have a basis of functions.
Give a basis for the kernel, you may enter a 0 in any box you believe you don't need.

2. Relevant equations

3. The attempt at a solution

I have little idea how to approach this problem. I know how to find the kernel and rank of a matrix transformation, but not a differential equation.

Last edited by a moderator: May 6, 2017
2. May 4, 2012

### clamtrox

Kernel of any linear operator is defined in exactly the same way:
$$\ker(T) = \lbrace y \in X | T(y) = 0 \rbrace$$
In this case, X is the space of all (smooth enough) functions, and you need to find those which satisfy T(y) = 0.

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