Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $F:\mathbb{R}^n\longrightarrow \mathbb{R}^m$ be a linear surjective map with $n \geq m$, if we denote by $A$ the matrix of $F$,is it true that the rank of $A$ is always $\neq 0$? Why?What can we say about the columns or lines of $A$?

Thanks.

share|improve this question
2  
Rank is the dimension of the range. If the map is surjective, what is the range? What is the dimension of the codomain? –  Bill Cook Feb 14 '12 at 22:08
add comment

1 Answer 1

up vote 1 down vote accepted

Hints:

1) $A$ is the $m\times n$ matrix such that $F(x)=A(x)$.

2) The range of $F$ is the column space of $A$.

3) The rank of $A$ is the dimension of its row space.

4) For any matrix $A$, the rank of $A$ is equal to the dimension of the column space of $A$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.