There are a lot of sites that have reliability statistics about vehicles. I think msn.autos list common problems and typical costs for the repair of those problems.

One big factor is the price of the parts.   Parts for vehicles that were produced in large numbers are generally cheaper.  So you should expect parts for a Nissan GTR to be more expensive then a Versa.  Also, parts for luxury vehicles are typically more expensive.  For example at GM, pricing for the same part at a Cadillac dealership is typically more expensive then a Chevy dealership. 

Another factor is your mechanic.  Dealership's are going to be far more pricey than local shops.  However, a poor mechanic anywhere is going to waste your time and money.  Look for ASE Certification.

Last, if you are buying used, then the previous owner is typically going to be a big factor as well.  Where they rough on the car?  Did they preform service at the recommended intervals?  Did they do repairs with cheap parts?  etc.

How to find out the "serviceability" of a car?

I got the following problem:

Let $A$ be a square matrix of order $n$ over field $\mathbb{F}$
and let $M_A$ be the minimal polynomial of $A$ of degree $k\in\mathbb{N}$ and let $0\neq c\in\mathbb{F}$ be any nonzero scalar in $\mathbb{F}$ then the minimal polynomial of $cA$ denoted by $M_{cA}$ is equal to
$c^nM_A({\frac tc})$ or $c^kM_A({\frac tc})$

I tried to prove it but didn't manage to continue that much.
 Thanks.
