Differentiate between consistent and Inconsistent system of linear equations. (2 Marks) b.) Discuss the consistency of the following system of equations and solve it, (12 Marks) i.) x +2y- z = 1 2x + y + 4z = 2 3x + 3y + 4z = 1 ii.) x+y+2z = 9 2x + y+ 2z = 1 3x + 6y- 5z =0 iii.) 2x - y = 5 x + 3y = 1 4x - 7y= 2 c.) i.) Show that the set of vectors In are linearly independent if X1, X2,..., and only if the equation - 1x1, A2X2, ..., An Xn only one solution a =a =...=an = 0 (3 Marks) 0 has one and ii.) Prove that the function cost and sine are linearly independent in the space [0, 2] of continuous functions. (3 Marks)