id: 06664664
dt: j
an: 2016f.01110
au: Carley, Holly
ti: On solving systems of equations by successive reduction using $2\times 2$
matrices.
so: Aust. Sr. Math. J. 28, No. 1, 43-56 (2014).
py: 2014
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: H60
ut: systems of equations; matrices; Cramer’s rule
ci:
li:
ab: Summary: Usually a student learns to solve a system of linear equations in
two ways: “substitution” and “elimination.” While the two
methods will of course lead to the same answer they are considered
different because the thinking process is different. In this paper the
author solves a system in these two ways to demonstrate the similarity
in the computation. She then sees that changing the point of view leads
to a “simpler” way to solve a system of equations. This leads
naturally to two other consequences, viz., what is known as Chio’s
pivotal condensation process for computing determinants and Cramer’s
Rule. While the condensation process for computing determinants is
known, it is not widely known, and the manner of solving equations
developed here has not been seen elsewhere. This should be of interest
to anyone teaching solving systems of linear equations (especially by
hand) and can be the basis for teaching the basics of solving systems
of equations, or for use as a guided project. This material is
particularly relevant for the topic of matrices in unit 2 of the
Specialist Mathematics, the topic of Algebra and matrices in unit 1 of
the General Mathematics curriculum, as well as anywhere where
multivariate applications appear such as finding regression lines in
the data collection topic in unit 3 of essential mathematics (perhaps
as a special project) and the bivariate data analysis topic of unit 3
of the general mathematics curriculum. (ERIC)
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