four vectors ~v1, ~v2, ~v3 and ~v4 be given by ~v1 = (1, 0, 2), ~v2 = (0, 1, −1), ~v3 = (1, 8, −6), ~v4 = (1, 2, 0); Let the vector space V be the linear span of ~v1, ~v2, ~v3 and ~v4. (a). Find all values of k such that the vector ~u = (2, 1, k) belongs to V . Explain. a.2)Are the vectors {~v1, ~v2} linearly independent? Explain. a.3)Find the dimension and a basis of the space V .

Let four vectors ~v1, ~v2, ~v3 and ~v4 be given by
~v1 = (1, 0, 2), ~v2 = (0, 1, −1),
~v3 = (1, 8, −6), ~v4 = (1, 2, 0);

Let the vector space V be the linear span of ~v1, ~v2, ~v3 and ~v4.
(a). Find all values of k such that the vector ~u = (2, 1, k) belongs to V .
Explain.

a.2)Are the vectors {~v1, ~v2} linearly independent? Explain.

a.3)Find the dimension and a basis of the space V .

a.4)Let A be the matrix whose columns are the vectors ~v1, ~v2, ~v3 and ~v4
(written as columns). Find a basis and the dimension of the solution
set of the homogeneous linear system AX = 0.

Please write full solution with clear work thank you!