System of Equations

Here's where matrices begin to get truly useful, even in the eyes of most students!

#### General Idea to Solving a System of Equations

First rewrite the equations into a matrix equation of the form

(1)
$$Ax=B$$

Where x is the matrix containing one column of variables and A is the matrix containing the coefficients of each variable. Use your GDC to find $A^{-1}$. Multiply both sides by the inverse:

(2)
$$A^{-1}Ax=A^{-1} B$$

The product of $A^{-1}$ and $A$ results in the identity matrix and a equation of the form:

(3)
$$x=A^{-1}B$$

Simply finish the matrix multiplication on the right side (use GDC) and then read off the values for each variable.