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)
\begin{equation} Ax=B \end{equation}

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)
\begin{equation} A^{-1}Ax=A^{-1} B \end{equation}

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

(3)
\begin{equation} x=A^{-1}B \end{equation}

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

Solving Systems of Equations 2 x 2

3 Equations and 3 Unknowns


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