# Linear algebra(linear transformation)

## Homework Statement

Let T be a Linear Transformation from U to V with dim(V)=m where m<infinity.

## Homework Equations

Show that rank(T) less than or equal to m.

## The Attempt at a Solution

Im really not that familiar with what rank or m is.

## Answers and Replies

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dextercioby
Homework Helper
Well, familiarity depends on your level of involvement. So look for the definition of <rank> in your notes/textbook. You can't find it (though i doubt it), search the internet: planetmath.org, wikipedia.org, wolfram sites offer a wealth of information on linear algebra.

m is the dimension of the vector space V. It's maximum number of linear independent vectors in V.

ok so rank is the max. number of linearly independent rows or columns.
I was trying to manipulate rank(T)=dim(range(T)) im not sure if this is the correct starting point?

dextercioby
Homework Helper
It is. What's range(T) equal to ?

No nevermind that belonged to another problem. Ok so i just have rank(T)+nullity(T)=m

It does not say what the range(T) is

dextercioby