The question is based on an exercise in linear algebra:
THOUGHTS:
By looking at the determinant, I know that a unique solution occurs when $c \neq 2$ or $-3$ since a square matrix is singular if and only if its determinant is $0$ (see this article). How can I really find what this solution is concretely?
Best Answer
Hint: The system has a unique solution if you can invert the matrix $$ \begin{bmatrix} 1&1&-1\\ 1&c&3\\ 2&3&c \end{bmatrix} $$ And the solution is $$ \begin{bmatrix} X_1\\X_2\\X_3 \end{bmatrix} = \begin{bmatrix} 1&1&-1\\ 1&c&3\\ 2&3&c \end{bmatrix}^{-1} \begin{bmatrix} 1\\2\\3 \end{bmatrix} $$