1. Linear independence and rank Consider 4 column vectors: , With r, y, ZER. i. Identify values of x, y, z such that the four vectors are linearly independent. Be sure to provide reasoning (e.g., along the lines of the statement in 4.1.4 of the Study Guide) and demonstrate that linear independence is satisfied. ii. Identify values of x, y, z such that the four vectors are linearly dependent, but any three of the vectors taken together are linearly independent. iii. In part (ii), showing the rank of the 4 x 4 matrix formed from your vectors to be 3 would not generally be a sufficient argument. Why not? 5 marks