Span of vectors in R3 1. The problem statement, all variables and given/known data u1 = (1,0,-1) u2 = (1,1,1) u3 = (3,1,-1) Determine whether the vectors span R^3. 2. Relevant equations 3. The attempt at a solution I know how to determine if the vectors span R^3(or maybe i dont). In this case checking if I can find a linear combo for (1,0,0) Step 1: 1 = a + b + 3c 0 = 0 + b + c 0 = -a + b - c Step 2: b = -c Step 3: 1 = a - c + 3c 1 = a + 2c Step 4: a = b -c a = -2c Step 5: 1 = (-2c) + 2c 1 = 0 Now with 1 = 0, I would think that the linear system of equations cannot be solved. **Solving this problem with my graphing calculator I get the same answer, however my book states that these three vectors do indeed span R^3. Why is that?