Originally Posted by
galactus First, write it in matrix format using the coefficients.
$\displaystyle \left[\begin{array}{ccc|c}1&5&6&10\\3&15&-2&9\\5&12&-9&5\end{array}\right]$
The idea is to use elementary row operations to hammer it into the form:
$\displaystyle \left[\begin{array}{ccc|c}1&0&0&a\\0&1&0&b\\0&0&1&c\end{ array}\right]$
Your solutions will be a,b, and c.
I feel about Gaussian eleimination the way Plato feels about partial fraction decompositions. With the technology that abounds these days, why go through the tedium of reduced row echelon?. We can spend our mathematical time more efficiently. But, you gotta do what you gotta do.
It took my TI about 2 seconds to give me:
$\displaystyle \left[\begin{array}{ccc|c}1&0&0&\frac{557}{260}\\0&1&0&\ frac{81}{260}\\0&0&1&\frac{21}{20}\end{array}\righ t]$