Notes: how do you solve simultaneous equations using matrices?

Sunday, January 18, 2015

To solve simultaneous equations using matrices we can use
Cramer's Rule.

Let us consider a set of two simultaneous
equations.

ax + by = e and cx + dy =
f

In matrix notation the equations are written
as:

$\displaystyle\lceil$ a b $\displaystyle\rceil$ $\displaystyle\lceil$ x $\displaystyle\rceil$ = $\displaystyle\lceil$ e
$\displaystyle\rceil$

$\displaystyle\lfloor$ c d $\displaystyle\rfloor$ $\displaystyle\lfloor$ y $\displaystyle\rfloor$ $\displaystyle\lfloor$ f
$\displaystyle\rfloor$

x = det [b e , f d] / det[a b , c
d]

y = det [a e , c f] / det[a b , c
d]

The method can be extended to be used for systems of
equations with a larger number of variables also.

Notes