Re: Matrices with Mathematica 5.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg63328] Re: [mg63315] Matrices with Mathematica 5.1*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 24 Dec 2005 07:18:54 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200512231008.FAA25936@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

If you want to maintain your entire 4-by-6 matrix intact, you need to write the matrix using Mathematica notation -- as a list of lists, using { and }, where the several lists are the rows of your matrix: A = {{1, 7, -2, 0, -8, -3}, {0, 0, 1, 1, 6, 5}, {0, 0, 0, 1, 3, 9}, {0, 0, 0, 0, 0, 0}} (If you don't like to type all those braces, you may use the entry Create Matrix/Table/Palette on the Input menu to provide a framework for typing the individual entries in a 2-dimensional grid. But, as the documentation for LinearSolve says, you need to use the form LinearSolve[mat,vec]. So you need to extract the first 5 columns to get the matrix, and the last column to get the "constants". Perhaps the quickest way to do that is to thing of applying the appropriate function on each row, e.g.: Most[{1, 7, -2, 0, -8, -3}] {1, 7, -2, 0, -8} Last[{1, 7, -2, 0, -8, -3}] -3 Now to do the same thing to all rows at once, use Map: Map[Most, A] {{1, 7, -2, 0, -8}, {0, 0, 1, 1, 6}, {0, 0, 0, 1, 3}, {0, 0, 0, 0, 0}} Map[Last, A] {-3, 5, 9, 0} Now you can either do those operations separately, assigning the results to two new names, e.g., coefficients = Map[Most, A] constants = Map[Last, A] and then just evaluate: LinearSolve[coefficients, constants] {-11, 0, -4, 9, 0} Or, probably, you would prefer to do the whole thing together, in one step. If so, to avoid distracting nested brackets, it's probably better to use the ... /@... input form for the Map function, that is, Most /@ A Last /@ A which mean the same thing as Map[Most, A] and Map[Last, A]. Then the whole thing, after you have your A, is done in one simple step as: LinearSolve[Most /@ A, Last /@ A] {-11, 0, -4, 9, 0} There are other, more awkward, means to extract all but the first column and to extract the last column. For example: 1. Keeping, still, with a "functional" approach in which you use Map, or its abbreviation /@ , to do the same operation to all rows in parallel, use the pure functions Drop[#, -1] & and Take[#, -1]& with Map to get the two arguments to LinearSolve. 2. Use indexing to get the coefficients and the constants (then use the results as the two arguments to LinearSolve). If you are coming from a more traditional and less expressive language than Mathematica, this is the version you might at first prefer: A[[ All, Range[5] ]] {{1, 7, -2, 0, -8}, {0, 0, 1, 1, 6}, {0, 0, 0, 1, 3}, {0, 0, 0, 0, 0}} A[[All, 6]] {-3, 5, 9, 0} In the Mathematica Front End, when typing those double brackets you'd probably want to precede and follow each with an Esc character, so that then they'd look like the tightly-spaced double brackets that more visibly indicate indexing and are not confused with ordinary brackets surrounding arguments. drizkol wrote: > I would like to solve the system given by: > > [1 7 -2 0 -8 -3] > [0 0 1 1 6 5] > [0 0 0 1 3 9] > [0 0 0 0 0 0] > > Where the matrix is a typical matrix in the form x1+x2+...+xn = b where > b is the last item in the row. For example, row 1 could be written as > x1 + 7x2 - 2x3 -8x4 = -3. How could I get mathematica to solve this > matrix? I understand how to build a matrix, I just need to know the > operation to run on it. I tried to use LinearSolve but I did something > wrong. Is there a built-in operation to solve these matrices? If so, > please tell. Thanks. > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Matrices with Mathematica 5.1***From:*"drizkol" <drizkol@gmail.com>