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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 u,   v,   w   are linearly independent.
b) Vectors u,   v,   w   are linearly dependent.
c) Vectors v,   w   are linearly dependent.
d) Vectors u,   v   are linearly dependent.
e) Vectors u,   w   are linearly independent.
Question 2. For which a∈ℝ   has the following system of linear equations no solution?

x+y-z=02x+2y+az=ay+z=a  

a) a=-2  
b) a=10  
c) it has a solution for all a∈ℝ  
d) a=3  
e) a=1  
Question 3. Determine the rank of the matrix (1,2,-2,-1,32,-3,1,1,41,9,-7,-4,5).  
a) 4
b) 2
c) 0
d) 1
e) 3

Evaluate