Linear Algebra and the C Language/a08o

__NOTOC__ Find a basis for ... Finding a basis for a row space of A by row reductions: The position of the pivots of Ab gives the position of the rows of A which form a basis for the row space of A. + Examples: * c00a.c * c00b.c * c00c.c * c00d.c Find a basis for the orthogonal complement of A: By calculating the free variables of the system Ab we will obtain this basis. + Examples: * c00a.c * c00b.c * c00c.c * c00d.c Finding a basis for a Column Space by Row Reduction :: The position of the pivots of Ab gives the position of the columns of A which form a basis for the column space of A. + Examples: * c00a.c * c00b.c * c00c.c * c00d.c Find a basis for the orthogonal complement of AT: The free vectors of the system BTb will be a basis for the orthogonal complement of AT, with B a basis of the column space of A. + Examples: * c00a.c * c00b.c * c00c.c * c00d.c