Re: Matrices with Mathematica 5.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg63327] Re: Matrices with Mathematica 5.1*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>*Date*: Sat, 24 Dec 2005 07:18:53 -0500 (EST)*Organization*: The Open University, Milton Keynes, U.K.*References*: <dogk9i$pqf$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"drizkol" <drizkol at gmail.com> a écrit dans le message de news: dogk9i$pqf$1 at smc.vnet.net... |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. | The above matrix is the _augmented_ matrix of the system of linear equations. For a system such as m . x == b, Mathematica built-in function *LinearSolve* expects two arguments: a matrix m of coefficients of x (a 5 x 4 matrix in your case) and a column vector b (a 4 x 1 vector in your case) corresponding to the values of the RHS of the system. Therefore, In[1]:= m = {{1, 7, -2, 0, -8}, {0, 0, 1, 1, 6}, {0, 0, 0, 1, 3}, {0, 0, 0, 0, 0}}; In[2]:= b = {{-3}, {5}, {9}, {0}}; In[3]:= x = LinearSolve[m, b] Out[3]= {{-11}, {0}, {-4}, {9}, {0}} In[4]:= m . x == b Out[4]= True will do it. Best regards, /J.M.