Find the Kernel T[[x],[y]]=[[x],[y]]

Problem

T*[[x],[y]]=[[x],[y]]

Solution

1. Identify the definition of the kernel of a linear transformation T which is the set of all vectors v such that T(v)=0

2. Set up the equation by setting the output of the transformation equal to the zero vector.

[[x],[y]]=[[0],[0]]

3. Solve the resulting system of equations for the variables x and y

x=0

y=0

4. Conclude that the only vector in the kernel is the zero vector, meaning the kernel is the trivial subspace.

Final Answer

ker(T)={[0],[0]}

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