 Frederick Kramer

2022-07-01

Suppose I were to be given 3 equations involving variables a, b, and c. The goal of the problem is to find the number of solutions (they do not necessarily have to be real) for the system of equations. Would it be more logical to use Cramer's Rule to solve the linear system or to use basic algebra? A roadmap of the following example problem or the like would be helpful.
A basic system taken from the book would be:
$\left\{\begin{array}{l}3a+4y-z=4\\ 3a+2b-11c=-13\\ a+2b+3c=7\end{array}$ Darrell Valencia

Expert

There are several good ways to solve systems of linear equations, and the best method to use in any given situation is the one that requires the least amount of work. However, that will depend on the particular equations that you’re trying to solve.
Generally linear algebra offer more useful techniques especially if the matrix has some special structure.
In your case, for example, the Rouché-Capelli theorem says that there are infinite solutions with 1 degree of freedom. fythynwyrk0

Expert