What is the dimension of its kernel?

[Jennifer1990]

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?

Homework Equations

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?

 

[Mark44]

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.

 

[Jennifer1990]

ohhhhh is it m - n?

 

[Dick]

Very likely it is.