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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page revision: 14, last edited: 30 Mar 2012 04:51
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