1. The problem statement, all variables and given/known data Determine if b is a linear combination of a1, a2, and a3. a1= [1,-2, 0] a2 = [0, 1, 2] a3 = [5, -6 8] b= [2, -1, 6] 3. The attempt at a solution Alright, well I used an augmented matrix to solve the problem, and after reducing it completely, the matrix looked like this: | 1 0 5 |2| | 0 1 4 |3| | 0 0 0 |0| Solving for the c's, I got: (Where the number to the right of the c denote which one instead of a multiplication number) c1+ 5c3=2 c2+4c3=3 0c3=0 I found that b is a combination of a1 and a2 if c3 is set to 0, however, since c3 is a free variable, and therefore can be anything, then b wouldn't be a lin. combination if c3 be anything other than 0. I'm having a hard time understanding this. Is it not a linear combination because there are other possible answers that wouldn't make it so? Or is it a linear combination because atleast one possibility works. Thank you for any help.