|Re: Error found on HP49G|
Message #2 Posted by William L. Drylie on 5 May 2000, 4:12 p.m.,
in response to message #1 by Aharon Sarussi
Dear Aharon: I do not have a 49G calculator, but I put your equation 6X-3Y=15 2X+Y=0 into a 48GX solve for linear equations and came up with the answer that you did X=1.8 and Y=0.9. Here is your explanation. First off in general, the solution set for a system of two equations in two variables is one ordered pair, an infinite number of ordered pairs or an empty set. This equation solution is an infinite number of ordered pairs, and the 48 and 49 will give you this answer if you investigate further. Right off the bat, you should enter the equations in matrix form on the stack, press MTH MATR NORM COND (hp 48G,GX) and compute its condition number. If it is large, 10 to the 12th power or higher, then it is an ill conditioned matrix. In this case with the above equation, it returns a condition error infinite results. Meaning, there are infinitely many ordered pairs. I'm sure the hp49G has the same tests. With this test, you can determine before hand if the equation is solvable with one specific ordered pair. If you do solve it first without testing, there is also another way to test. Your hp 49 returned an answer to you that was not useable because it returned the smallest ordered pair that it could obtain, basically it returned one of the infinite pairs as an answer. Finding the residual of the array will verify this. I will not go into these instructions as I do not have a 49G but I'm sure it has a test for the residual of an array or matrix. The smaller the absolute value of the elements the better the solution, in this case on my 48GX it was rather high. So it is up to the individual to test the answer they receive from the calculator for validity. This is true in both the 48&49. In the hp48GX manual it says that the Linear system solver will return a result array for any of the following systems. Exactly determined systems, Over determined sytems, or under determined sytems, and goes on to say to pay attention to your linear system because it will influence the way you should interpret the result array, and to test for ill conditioning before you solve, or even accept an exact solution as a valid solution. No bug! Hope I have helped you.