Question

3. Show, by inspection (without forming a matrix), that the given vectors are linearly dependent. vi = (1, -1,0,1), v2 = (1,1,1,0), 3 = (1,2,0,1), 74 = (-1, -2, 1,0) 2 -1 ::: - سه 4. Let S = 6 3 Is S a basis for R?? Explain your answer. 0 0

Answer 1

co V- 2 To Vz VA - 2 o O Since. Vit V₂ - V3 = V4 ine. Va can be Linear combination of UV₂, V3 written as Vectors are Linear gudependent. (L. I.) S = {lo\.(3)47) matrix form 2 4. 6 3 4 0 R₂ - Ra -3Rl 2 -4 16 1 We are Since the matrix matrix has full rank full rank o vectors L.I. & know and L.I. set in elements form a basis for R". so s will be basis for R² Am Containing