how do you solve simultaneous equations using matrices?
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:
`|~` a b `~|` `|~`x`~|` = `|~` e `~|`
`|__` c d `__|` `|__`y`__|` `|__` f `__|`
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.