Question

How do you solve a simultaneous equation using matrices?

Answer 1

Write the equations as matrices.
Multiply both sides by the inverse matrix of the coefficients.

Explanation:

Here is the general principal, without using an actual example.

Equations such as `ax +by= c" "and" " dx+ey =f`

can be written as matrices:

`" "((a,b),(d,e))((x),(y)) = ((c),(f))`

A matrix multiplied by its inverse gives the unit or identity matrix
which is `((1,0),(0,1))`

Multiplying by this matrix has the same result as multiplying by `1`.

Let `M^-1` be the inverse of `((a,b),(d,e))`

Find this inverse matrix.

Then multiplying both sides by `M^-1` gives:

`M^-1((a,b),(d,e))((x),(y)) = M^-1((c),(f))`

`((x),(y)) = M^-1((c),(f))`

When you multiply the right side you will have the values for `x and y` in the resulting matrix.