From: dslowik <dslowik_at_tellink.net>

Date: Sat, 21 May 2011 18:34:20 -0700 (PDT)

Date: Sat, 21 May 2011 18:34:20 -0700 (PDT)

I have a simple system of linear equations to solve for X, aX=b:
> a

[,1] [,2] [,3] [,4]

*[1,] 1 2 1 1
**[2,] 3 0 0 4
*

[3,] 1 -4 -2 -2

[4,] 0 0 0 0

> b

[,1]

[1,] 0

*[2,] 2
**[3,] 2
**[4,] 0
*

(This is ex Ch1, 2.2 of Artin, Algebra).
So, 3 eqs in 4 unknowns. One can easily use row-reductions to find a
homogeneous solution(b=0) of:

X_1 = 0, X_2 = -c/2, X_3 = c, X_4 = 0

and solutions of the above system are:

X_1 = 2/3, X_2 = -1/3-c/2, X_3 = c, X_4 = 0.

So the Kernel is 1-D spanned by X_2 = -X_3 /2, (nulliity=1), rank is 3.

In R I use solve():

> solve(a,b)

Error in solve.default(a, b) :

Lapack routine dgesv: system is exactly singular

and it gives the error that the system is exactly singular, since it seems
to be trying to invert a.

So my question is:

Can R only solve non-singular linear systems? If not, what routine should I
be using? If so, why? It seems that it would be simple and useful enough to
have a routine which, given a system as above, returns the null-space
(kernel) and the particular solution.

-- View this message in context: http://r.789695.n4.nabble.com/Finding-solution-set-of-system-of-linear-equations-tp3541490p3541490.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Sun 22 May 2011 - 02:36:32 GMT

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