1. The problem statement, all variables and given/known data Determine whether the given vectors span R3: v1=(3,1,4) v2=(2,-3,5) v3=(5,-2,9) v4=(1,4,-1) 2. Relevant equations I need to show that an arbitrary point in R3 can be written as: (b1,b2,b3)=k1(3,1,4)+k2(2,-3,5)+k3(5,-2,9)+k4(1,4,-1) 3. The attempt at a solution I know that when you have 3 different vectors and have to work out if they span R3 you can write the coefficient matrix and find out if the determinant of that matrix is equal to zero or not. Therefore I know that: 3k1 + 2k2 + 5k3 + k4 = b1 k1 + (-3)k2 + (-2)k3 + 4k4 = b2 4k1 + 5k2 + 9k3 + (-1)k4 = b3 Since this augmented matrix is 3x4 I can't use the determinant method I used before (unless I use a long-winded method of working out if 3 vectors span at a time). I apologise if this is quite basic I am only just learning about vector spaces!