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curriculum/challenges/italian/10-coding-interview-prep/rosetta-code/cramers-rule.md
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---
id: 59713da0a428c1a62d7db430
title: Cramer's rule
title: Regola di Cramer
challengeType: 5
forumTopicId: 302239
dashedName: cramers-rule
@ -8,43 +8,43 @@ dashedName: cramers-rule
# --description--
In [linear algebra](https://en.wikipedia.org/wiki/linear algebra "wp: linear algebra"), [Cramer's rule](https://en.wikipedia.org/wiki/Cramer's rule "wp: Cramer's rule") is an explicit formula for the solution of a [system of linear equations](https://en.wikipedia.org/wiki/system of linear equations "wp: system of linear equations") with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right hand sides of the equations.
In <a href="https://it.wikipedia.org/wiki/Algebra_lineare"">algebra lineare</a>, la [regola di Cramer](https://it.wikipedia.org/wiki/Regola_di_Cramer "wp: Regola di Cramer") è una formula esplicita per la risoluzione di un [sistema di equazioni lineari](https://it.wikipedia.org/wiki/Sistema_di_equazioni_lineari) con tante soluzioni quante sono le variabili, valida ogni volta che il sistema ha una soluzione unica. Esprime la soluzione in termine di determinanti della matrice quadrata dei coefficienti e delle matrici ottenute da essa sostituendo una delle colonne con il vettore dei termini a destra dell'uguale nelle equazioni.
Given
Dati
$\\left\\{\\begin{matrix}a_1x + b_1y + c_1z&= {\\color{red}d_1}\\\\a_2x + b_2y + c_2z&= {\\color{red}d_2}\\\\a_3x + b_3y + c_3z&= {\\color{red}d_3}\\end{matrix}\\right.$
which in matrix format is
che in forma matriciale è
$\\begin{bmatrix} a_1 & b_1 & c_1 \\\\ a_2 & b_2 & c_2 \\\\ a_3 & b_3 & c_3 \\end{bmatrix}\\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix}=\\begin{bmatrix} {\\color{red}d_1} \\\\ {\\color{red}d_2} \\\\ {\\color{red}d_3} \\end{bmatrix}.$
Then the values of $x, y$ and $z$ can be found as follows:
Allora i valodi di $x, y$ e $z$ possono essere trovati come segue:
$x = \\frac{\\begin{vmatrix} {\\color{red}d_1} & b_1 & c_1 \\\\ {\\color{red}d_2} & b_2 & c_2 \\\\ {\\color{red}d_3} & b_3 & c_3 \\end{vmatrix} } { \\begin{vmatrix} a_1 & b_1 & c_1 \\\\ a_2 & b_2 & c_2 \\\\ a_3 & b_3 & c_3 \\end{vmatrix}}, \\quad y = \\frac {\\begin{vmatrix} a_1 & {\\color{red}d_1} & c_1 \\\\ a_2 & {\\color{red}d_2} & c_2 \\\\ a_3 & {\\color{red}d_3} & c_3 \\end{vmatrix}} {\\begin{vmatrix} a_1 & b_1 & c_1 \\\\ a_2 & b_2 & c_2 \\\\ a_3 & b_3 & c_3 \\end{vmatrix}}, \\text{ and }z = \\frac { \\begin{vmatrix} a_1 & b_1 & {\\color{red}d_1} \\\\ a_2 & b_2 & {\\color{red}d_2} \\\\ a_3 & b_3 & {\\color{red}d_3} \\end{vmatrix}} {\\begin{vmatrix} a_1 & b_1 & c_1 \\\\ a_2 & b_2 & c_2 \\\\ a_3 & b_3 & c_3 \\end{vmatrix} }.$
# --instructions--
Given the following system of equations:
Dato il seguente sistema di equazioni:
$\\begin{cases} 2w-x+5y+z=-3 \\\\ 3w+2x+2y-6z=-32 \\\\ w+3x+3y-z=-47 \\\\ 5w-2x-3y+3z=49 \\\\ \\end{cases}$
solve for $w$, $x$, $y$ and $z$, using Cramer's rule.
risolvi per $w$, $x$, $y$ e $z$, usando la regola di Cramer.
# --hints--
`cramersRule` should be a function.
`cramersRule` dovrebbe essere una funzione.
```js
assert(typeof cramersRule === 'function');
```
`cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])` should return `[2, -12, -4, 1]`.
`cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])` dovrebbe restituire `[2, -12, -4, 1]`.
```js
assert.deepEqual(cramersRule(matrices[0], freeTerms[0]), answers[0]);
```
`cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])` should return `[1, 1, -1]`.
`cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])` dovrebbe restituire `[1, 1, -1]`.
```js
assert.deepEqual(cramersRule(matrices[1], freeTerms[1]), answers[1]);