
06012437
j
2012b.00834
Dobbs, David E.
On rank and nullity.
Int. J. Math. Educ. Sci. Technol. 43, No. 2, 271283 (2012).
2012
Taylor \& Francis, Abingdon, Oxfordshire
EN
H65
matrices
field
row rank
column rank
nullity
system of linear equations
Cramer's rule
determinants
doi:10.1080/0020739X.2011.582181
Summary: This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.