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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: 20,373 Thanks: 2009 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: 20,373 Thanks: 2009 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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