hi guys!

need help for this!

In each case below show that the statement is True or give an example showing that it is False. (i) If {X, Y, Z} is independent in R", then aX + by + cZ =0 for some a, b, c E R. (ii) If {X, Y} is independent in R", then {X, Y, X + Y} is independent. (iii) If {Y, Z} is dependent in R", then {X, Y, Z } is dependent. (iv) If {X1, X2, ..., Xx} C R", is independent, and Y @ span {X1, X2, . .. , Xx}, then {X1, X2, ..., Xk, Y} is independent. (v) If A is an m x n matrix and rank A = m, then m