Multiple-choice question

[TCruz12]

What is the strongest statement you can make about the number of free variables in a 4×6 coefficient matrix, when row-reduced?
The number of free variables must be either:
a. exactly _____
b. at most _____
c. at least ______

 

[HallsofIvy]

A "4x6 coefficient matrix" is equivalent to 4 equations in 6 unknowns. If the equations are independent then we could solve for 4 of the unknowns in terms of the other two so the number of free variables is 2. What if they are NOT independent?

 

[Steven G]

Wait I know this answer. They are dependent(?)

 

[HallsofIvy]

What is this responding to? What are dependent?

 

[TCruz12]

So, would the answer be Exactly 2?