[R] Solving Matrices

[Gabor Grothendieck]

 <wettenhall <at> wehi.EDU.AU> writes:

: 
: On April 15th, Elizabeth wrote:
: <snip>
: >      In execises 39-42, determine if the columns of the matrix span
: >      R4:
: <snip>
: >(or x <- matrix(data=c(7, -5, 6, -7, 2, -3, 10, 9, -5,
: >                        4, -2, 2, 8, -9, 7, 15), nrow=4, ncol=4)
: >
: >That is the whole of the question <snip>
: 
: Have you tried det(x) and/or eigen(x) ?
: 
: A zero determinant (within computer precision) means that the matrix does
: not have full rank, i.e. it does not span R4.  

In this case we can avoid the computer precision problem by noting
that the determinant of an integer matrix is always integer, so:

   round(det(x))

will be non-zero iff the square integer matrix x is of full rank.