I've been playing with the matrix functions, doing Gaussian elimination
and such, and I ran across something I don't understand. The function
"augcoefmatrix" takes a set of linear equations and returns the
coefficient matrix augmented by the column vector of constants in the
equations. The strange part is, the augmenting column is the negative
of the constant vector. For example:
(%i1) augcoefmatrix([x1+2*x2+x3=4, 2*x1-x2-x3=1, x1+x2+x3=0],
[x1,x2,x3]);
[ 1 2 1 - 4 ]
[ ]
(%o1) [ 2 - 1 - 1 - 1 ]
[ ]
[ 1 1 1 0 ]
The documentation of the function makes no mention of this. Is there
some convention, or ease of interface, at play here? I checked a linear
algebra text, a text on matrix methods, a text on numerical methods, and
Wikipedia; none mentioned anything like the negatives of the constants
being useful or used by some authors.
so ... what's up?
-- Bill Wood