Question about the dimensions

[Frandom]

Hello to all !

I have an exercice and the answer, but without any explanation. I cannot understand why this is the correct answer ! Anyone to help me ?

Here is the exercice :

Suppose we have an expression of the form Ax=B where x is a 7-dimensional vector and A is a 5X7 matrix. Which of the following is correct ?

A. dim(col(A))>=5.
B. dim(col(A))=<2.
C. dim(Nul(A))>=2. (correct answer)
D. rank(A)=7.

Thank you a lot in advance !!!
Frandom.

 

[Steven G]

If there are 5 equations in 7 variables, then dim(nul(A)) >= 7-5.
You are in Linear Algebra--think about why this is true.
Giving you more than I did would not help you out. You need to see this on your own. Look at the problem from all different angles--sideways, upside down, inside out,.. . That is how you will learn abstract math.