How could I describe how solving a system of equations using Matrices is similar and different than solving an equation like 2x + 3 = 8 to NON MATH friends?
Hey Civy71.
You first have to understand linearity first off, since matrices are the most general form of linear objects.
Once you do this, you need to understand how a linear object (i.e. a matrix) transforms a vector or another linear object with certain properties (through matrix multiplication).
By explaining things in terms of rotations, scaling, and translations, you can explain how an inverse matrix "undoes" what a non-inverse matrix did.
This is the geometric idea behind a matrix (i.e. a linear operator) and depending on the operator, you can undo these things (i.e. a square matrix with non-zero determinant) and get back your original vector.