Are the columns linear independent?

[lastlanding]

Homework Statement

Were the columns of A linearly independent?
The matrix A is given in row reduced echeleon form
1 2 0 0
0 0 1 0
0 0 0 1

Homework Equations

Hint: Consider the solution set to A x = 0

The Attempt at a Solution

I think that the colums were linearly dependent since the first two columns in their row reduced forms are multiple of each other. Is that correct? If yes, and my explanation seems logical, then why is the hint given?

 

[vela]

Perhaps they want you to see why "the first two columns in their row reduced forms are multiple of each other" implies that the columns of A are linearly dependent. In other words, the definition of linear independence says the vectors v1, v2, v3, and v4 are independent if the only solution of c1 v1+c2 v2+c3 v3+c4 v4=0 is c1=c2=c3=c4=0. How does what you said about the row-reduced matrix lead to the conclusion that the original columns of A are linearly dependent according to the definition above?