Geometric description of kernel

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T is the projection onto the xy-coordinate plane:
T(x,y,z)=(x,y,0)

I have to give a geometric description of the kernel and range of T.


my geometric description of the kernel:
a line along the z-axis. Is this correct?
whats the geometric description of the range of T?
 
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Why "a line along the z-axis". Why not just "the z-axis"?

Is not the range, the set of all pairs (x,y, 0) pretty obvious?
 

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