 My Math Forum Need some help with this vector equation

 Calculus Calculus Math Forum

 October 15th, 2018, 12:14 AM #1 Newbie   Joined: Sep 2018 From: Spain Posts: 19 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 01:35 AM. October 15th, 2018, 12:49 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 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, 01:16 AM #3 Newbie   Joined: Sep 2018 From: Spain Posts: 19 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 01:34 AM. October 15th, 2018, 01:34 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 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. Tags equation, vector Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post pass92 Calculus 1 November 24th, 2016 03:01 PM JJS Abstract Algebra 1 November 26th, 2015 03:58 AM chocolatesheep Linear Algebra 0 September 25th, 2014 11:22 AM marks2014 Geometry 3 May 16th, 2014 01:43 PM luketapis Algebra 2 November 22nd, 2011 06:53 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      