finite duration signal

[logistic_guy]

here is the question

Consider the finite-duration signal $\displaystyle x(n) = \{1,2,3,1\}$.

(a) Compute its four-point DFT by solving explicitly the $\displaystyle 4$-by-$\displaystyle 4$ system of linear equations defined by the inverse DFT formula.
(b) Check the answer in part (a) by computing the four-point DFT, using its definition.


my attemb
how to use the inverse DFT formula to construct $\displaystyle 4\times 4$ matrix?
$\displaystyle x(n) = \frac{1}{N}\sum_{k=0}^{N-1}X(k)e^{j\frac{2\pi}{N}nk}$