Cramers Rule

A formula to find the solution to $A\overrightarrow{x}=\overrightarrow{b}$

Theorem

If $A$ is Isomorphic. Then, $x_i=\frac{\det (A_i)}{\det (A)}$ where:

• $x_i$ is the $i-th$ column of $x$
• $A_i$ is the matrix formed by replacing the $i-th$ column of $A$ with $\overrightarrow{b}$

Example