Simultaneous Equation mini-challenge « Next Oldest | Next Newest »

 ▼ Rodger Rosenbaum Senior Member Posts: 305 Threads: 17 Joined: Jun 2007 03-31-2006, 01:52 AM Quote: In his submission "Calculator Precision: Sure" of December 21 which started all of this Valentin Albillo proposed an investigation of the set of linear equations 1.3 x1 + 7.2 x2 + 5.7 x3 + 9.4 x4 + 9.0 x5 + 9.2 x6 + 3.5 x7 = 45.3 4.0 x1 + 9.3 x2 + 9.0 x3 + 9.9 x4 + 0.1 x5 + 9.5 x6 + 6.6 x7 = 48.4 4.8 x1 + 9.1 x2 + 7.1 x3 + 4.8 x4 + 9.3 x5 + 3.2 x6 + 6.7 x7 = 45.0 0.7 x1 + 9.3 x2 + 2.9 x3 + 0.2 x4 + 2.4 x5 + 2.4 x6 + 0.7 x7 = 18.6 4.1 x1 + 8.4 x2 + 4.4 x3 + 4.0 x4 + 8.2 x5 + 2.7 x6 + 4.9 x7 = 36.7 0.3 x1 + 7.2 x2 + 0.6 x3 + 3.3 x4 + 9.7 x5 + 3.4 x6 + 0.4 x7 = 24.9 4.3 x1 + 8.2 x2 + 6.6 x3 + 4.3 x4 + 8.3 x5 + 2.9 x6 + 6.1 x7 = 40.7 which has the "unique" solution : x1 = x2 = x3 = x4 = x5 = x6 = x7 = 1.0 Consider a linear system, Ax = B, where B is an all zeroes vector; in other words, the system Ax = 0. One obvious solution is x=0; this is called the trivial solution. We learn in linear algebra that the Ax = 0 system only has a solution if A is singular. Valentin's A matrix is almost singular, so maybe there is an approximate solution. Find a solution vector x with length 1 (use the ABS function on the HP49G+) that gives a result A*x that is the smallest possible.

 Possibly Related Threads... Thread Author Replies Views Last Post Equation Library/App for the Prime Harold A Climer 3 622 10-30-2013, 10:14 AM Last Post: CompSystems Equation Library on the PRIME Harold A Climer 0 357 10-26-2013, 10:01 AM Last Post: Harold A Climer Meltiple Equation Solver PRIME Vs. HP 50G Harold A Climer 5 713 10-07-2013, 05:11 PM Last Post: CR Haeger EOT--TI N-Spire Equation Limit Matt Agajanian 2 476 09-22-2013, 12:37 PM Last Post: Matt Agajanian Does Prime Have a Multiple Equation Solver? Norman Dziedzic 2 454 09-20-2013, 09:43 AM Last Post: Norman Dziedzic Equation of the parabola given three points Gerson W. Barbosa 27 2,284 09-18-2013, 01:58 PM Last Post: Gerson W. Barbosa HPCC Mini Conference 2013 hugh steers 6 770 09-13-2013, 04:27 PM Last Post: BruceH Picture from the Mini-HHC (LA) Geir Isene 11 1,086 07-07-2013, 01:06 PM Last Post: Jim Horn HP 50g: Customize Your Equation Library Software49g 2 500 05-27-2013, 12:39 PM Last Post: Software49g A very long HP-17BII equation Gerson W. Barbosa 22 2,104 04-19-2013, 12:37 AM Last Post: Gerson W. Barbosa

Forum Jump: 