Determine whether the vectors u=(1,−1,2)\mathbf{u} = (1, -1, 2)u=(1,−1,2), v=(2,0,3)\mathbf{v} = (2, 0, 3)v=(2,0,3), w=(0,1,−12)\mathbf{w} = (0, 1, -\frac{1}{2})w=(0,1,−21) in R3\mathbb{R}^3R3 are linearly independent.
Yes, because det([u,v,w])≠0\det([\mathbf{u}, \mathbf{v}, \mathbf{w}]) \neq 0det([u,v,w])=0
No, because det([u,v,w])=0\det([\mathbf{u}, \mathbf{v}, \mathbf{w}]) = 0det([u,v,w])=0
Yes, because each vector is non-zero
Cannot determine without additional information