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October 14th, 2018, 11:14 PM  #1 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0  Need some help with this vector equation
Write the vector v1= (3, 2) as a linear combination of the vectors v2 = (1, 3) and V3 = (1, 0). All of the (V)'s have this at the top of it >. The answers they got were v1 = 2/3v2  11/3v3. I am trying to wonder how they came up with that conclusion. Someone please explain it to me. Thank you! Last edited by skipjack; October 15th, 2018 at 12:35 AM. 
October 14th, 2018, 11:49 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,831 Thanks: 2161 
By inspection, 3v1 + 2v2 = (3*3 + 2, 3*2 + 2*3) = (11, 0) = 11v3. Hence v1 = (2v2  11v3)/3 = 2/3v2  11/3v3. 
October 15th, 2018, 12:16 AM  #3 
Newbie Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0 
Hi, thanks skipjack, but can you explain what's the process or the formula for solving this type of equation? Because I am confused as to how you got the 3v1 + 2v2.
Last edited by skipjack; October 15th, 2018 at 12:34 AM. 
October 15th, 2018, 12:34 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,831 Thanks: 2161 
It was easy to see that multiplying v1 by 3 and v2 by 2 would lead to a multiple of v3. Alternatively, solve a(1, 3) + b(1, 0) = (3, 2), i.e. a  b = 3 and 3a + 0b = 2. The second equation implies a = 2/3. The first equation implies b = a  3 = 11/3. Any other method of solving simultaneous linear equations could be used. 

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