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.