R help - Aug 2006 - singular matrix

Dear R-users,
I try to use "solve" to get the solution of this matrix.But it has
error
happen below.
How  I can solve this problem. 
[1] "a"
          [,1]
[1,] 0.8109437
[2,] 5.7569740
[1] "b"
          [,1]      [,2]
[1,] 0.3141293  2.230037
[2,] 2.2300367 15.831264

Error in solve.default(b, a) : system is computationally singular:
reciprocal condition number = 1.37415e-018

Thanks 
Luck

Nongluck Klibbua reports:
> -----Original Message----- 
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nongluck
> Klibbua
> Sent: Tuesday, 29 August 2006 11:12 AM
> To: R-help at stat.math.ethz.ch
> Subject: [R] singular matrix
> 
> Dear R-users,
> I try to use "solve" to get the solution of this matrix.But it
has
error
> happen below.
> How  I can solve this problem. 
> [1] "a"
> 	    [,1]
> [1,] 0.8109437
> [2,] 5.7569740
> [1] "b"
> 	    [,1]      [,2]
> [1,] 0.3141293  2.230037
> [2,] 2.2300367 15.831264
> 
> Error in solve.default(b, a) : system is computationally singular:
> reciprocal condition number = 1.37415e-018
The irony seems to be that if you quote them to only this number of
digits then the system is no longer quite singular enough for the
problem to appear, at least on Windows R 2.3.1:
> a
          [,1]
[1,] 0.8109437
[2,] 5.7569740
> b
          [,1]      [,2]
[1,] 0.3141293  2.230037
[2,] 2.2300367 15.831264
> solve(b, a)
              [,1]
[1,]  2.5831242104
[2,] -0.0002203103
> b %*% solve(b, a) - a  ### check
              [,1]
[1,] -1.110223e-16
[2,] -8.881784e-16

In general, though, in dealing with singular systems you might want to
look at the function ginv in the MASS library.

b is nearly singular.  Note that one of its eigenvalues is -2.935e-8
which is close to zero.  We can use the generalized inverse from
MASS to get one solution, x, but any multiple of the eigenvector
corresponding to the near-zero eigenvalue when added to that
will also give a solution as shown:
> eigen(b)
$values
[1]  1.614539e+01 -2.935343e-08

$vectors
           [,1]       [,2]
[1,] -0.1394858 -0.9902241
[2,] -0.9902241  0.1394858
> library(MASS)
> x <- ginv(b) %*% a
> a
[1] 0.8109437 5.7569740
> # bx gives a showing x is a solution
> b %*% x
          [,1]
[1,] 0.8109438
[2,] 5.7569740
> # but b(x + e) where e is 2nd eigenvector is also solution
> b %*% (x + eigen(b)$vectors[,2])
          [,1]
[1,] 0.8109438
[2,] 5.7569740

On 8/28/06, Nongluck Klibbua <Nongluck.Klibbua at newcastle.edu.au>
wrote:
> Dear R-users,
> I try to use "solve" to get the solution of this matrix.But it
has error
> happen below.
> How  I can solve this problem.
> [1] "a"
>          [,1]
> [1,] 0.8109437
> [2,] 5.7569740
> [1] "b"
>          [,1]      [,2]
> [1,] 0.3141293  2.230037
> [2,] 2.2300367 15.831264
>
> Error in solve.default(b, a) : system is computationally singular:
> reciprocal condition number = 1.37415e-018
>
> Thanks
> Luck
>
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