How do you solve a simultaneous equation using matrices?

1 Answer
May 18, 2017

Answer:

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.