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October 25th, 2017, 08:19 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 100 Thanks: 2  Find a basis for the vectors over the reals:
the vectors are (1+i) (1i) (2+3i) where the vectors are complex numbers that span the reals. Do i just have to set up a system of equations and row reduce it to find the basis vectors and find the rank of the system? Or could i just put coefficients infront of the vectors and set it equal to 0 to test for linear independance, thanks 
October 25th, 2017, 08:43 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,169 Thanks: 1141 
This is a very confusing post. Could you post the original question as worded? 
October 25th, 2017, 11:48 AM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 502 Thanks: 280 Math Focus: Dynamical systems, analytic function theory, numerics 
$\mathbb{C}$ is a 2 dimensional vector space over $\mathbb{R}$ which means any 2 linearly independent vectors is a basis. I don't understand what the role of the 3 vectors you have supplied is. The span of those 3 vectors is identical to $\mathbb{C}$ (as a vector space) but this is true for only a pair of them or any other linearly independent pair for that matter. 

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