What is the dimension of its kernel?

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Homework Statement


Suppose that dim V = m and dim W = n with M>=n . If the linear map A : V -> W is onto, what is the dimension of its kernel?



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The Attempt at a Solution


Onto, means that every vector in W has at least one pre-image therefore, the kernel can have a maximum dimension of m?
 
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There is a property that you can use: dim(ker A) + dim(im A) = dim V. (see http://en.wikipedia.org/wiki/Kernel_(linear_operator )) The fact that A is onto W tells you something about dim(im A), the dimension of the image of A.
 
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ohhhhh is it m - n?
 


Very likely it is.
 
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