9. Suppose V1, V2, V3, V4 are linearly independent. Prove that the following vectors are also linearly independent - V1 V2, V2 - V3, V3 - V4, V4 10. Check if the following vectors are linearly independent or not: (a) (1, 1, 1), (1,2,3), (1, 5, 8) Є R³ (b) (1,2,0), (-1, 1, 2), (3, 0, −4) Є R³ (c) (−11,3,10), (1, −5, 26), (3, 4, −4), (1, 1, −1) Є R³ (d) sin(x), sin(2x) = C[-∞, ∞] (e) u = 2t23t+4, v = - (f) u = [1 1 [1] v = 2 2 2 " 4t2 [222] 333 3t+2 [333] w= ' 44 4 11. Determine if the vectors (1, 1, 1, 1), (1, 2, 3, 2), (2, 5, 6, 4), (2, 6, 8, 5) form a basis for R4. If not, find the dimension of the spanned subspace and basis for this subspace. (4.25)