Let V be a vector space over IF. Suppose that 1+1 = 0 in IF and the list v1,v2,v3,v4 is linearly independent in V . Show that the list v1 v2, v1 + v2, v3 v2, v4 v1 is also linearly independent in V .

Does the statement of Problem still hold if we replace 'linearly independent' by 'a basis'?

Prob 3. Let V be a vector space over IF. Suppose that 1 + 1 * 0 in IF and the list v1, V2, V3, v4 is linearly independent in V. Show that the list v1 - V2, V1 + 12, v3 - V2, 14 - v1 is also linearly independent in V.Prob 4. Does the statement of Problem 3 still hold if we replace 'linearly independent' by 'a basis' ? Prob 4. Does the statement of Problem 3 still hold if we replace 'linearly independent' by 'a basis