How do I solve a system of 3 equations with a matrix?

1 Answer
Gió
Dec 25, 2014

I would use Cramer's Rule .
This rule is based upon using the matrix associated with the coefficients of the unknowns and of the pure coefficients of your system, evaluate their determinants and combine them to evaluate the values of the unknowns.

Consider an example:

enter image source here

Now we consider 3 other matrices, #A_x, A_y and A_z# and their determinant. These matrices are obtained by substituting each column of #A# with the column of pure coefficients (the ones without unknown):

enter image source here

We evaluate the three determinants for these matrices:

enter image source here

Finally we can calculate the values of the unknowns as:

#x=det(A_x)/(det(A))=(-60)/-60=1#
#y=det(A_y)/(det(A))=(-240)/-60=4#
#z=det(A_z)/(det(A))=(120)/-60=-2#

Your final result is:
#x=1#
#y=4#
#z=-2#

Related questions
See all questions in Solving a System of Equations Using a Matrix
Impact of this question
11618 views around the world
You can reuse this answer
Creative Commons License