- #1

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## 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.

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- Thread starter chuy52506
- Start date

- #1

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

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

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

- #2

- 13,058

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

- #3

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I was trying to manipulate rank(T)=dim(range(T)) im not sure if this is the correct starting point?

- #4

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

- #5

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

- #6

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So once more: what's range (T) equal to ?

- #7

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It does not say what the range(T) is

- #8

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If U is a linear space and T is a linear operator, one can easily show that range(T) is also a linear space, namely a vector subspace of V.

- #9

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I think the rank-nullity theorem is exactly what you want to use.

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