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Question 1. Given vectors u=(2,-1,5),   v=(4,-2,0),   w=(-6,3,-15).   Decide which of the following is true.
a) Vectors v,   w   are linearly dependent.
b) Vectors u,   w   are linearly independent.
c) Vectors u,   v,   w   are linearly dependent.
d) Vectors u,   v   are linearly dependent.
e) Vectors u,   v,   w   are linearly independent.
Question 2. For which a∈ℝ   has the following system of linear equations a unique solution?

2x+2y-2z=0x+y+az=ay+z=a  

a) a=-1  
b) a≠-1  
c) for all a∈ℝ  
d) a≠12  
e) a=3  
Question 3. Determine the rank of the matrix   (1,-3,2,61,5,8,160,0,2,-1).                           
a) 4
b) 3
c) 2
d) 0
e) 1

Evaluate