Question: I'm studying a pre-calculus textbook and it mentioned this:

> 
> "It is important to note that not every relationship expressed by an
>  equation can also be expressed as a function with a formula."
> 
> 
> 

Can someone help me understand this by giving examples?

Answer: 
The matrix is $A=\begin{bmatrix} -c & 6 & 2 \\ 3 & -c & 2 \\ 1 & 2 & c \end{bmatrix}$.

The determinant is 
$\det A = -c(-c^2-4) -6 (3c-2)+2(6+c)$. Now factor and find values for $c$ for which the determinant is zero.
You have to solve the system
$$c\lambda\_1+6\lambda\_2+\lambda\_3=0$$
$$6\lambda\_1-c\lambda\_2+2\lambda\_3=0$$
$$\lambda\_1+2\lambda\_2+c\lambda\_3=0$$
for $\lambda\_1,\lambda\_2,\lambda\_3$