# Cramer’s rule

## Solutions

Solution 1 (Click to Show/Hide)
``````function determinant(matrix) {
const n = matrix.length;
switch (n) {
case 1:
return matrix[0][0];
case 2:
return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0];
case 3:
const a00 = matrix[1][1]*matrix[2][2] - matrix[1][2]*matrix[2][1];
const a01 = matrix[1][0]*matrix[2][2] - matrix[1][2]*matrix[2][0];
const a02 = matrix[1][0]*matrix[2][1] - matrix[1][1]*matrix[2][0];
return a00*matrix[0][0] - a01*matrix[0][1] + a02*matrix[0][2];
default:
// Recursive definition
let det = 0;
for (let i = 0; i < n; i++) {
const reducedMatrix = matrix.reduce(
(acc, row, j) => {
if (i !== j) {
const [_, ...rowCopy] = row;
acc.push(rowCopy);
}
return acc
},
[]
)
det += matrix[i][0]*determinant(reducedMatrix)*(i % 2 === 0 ? 1 : -1);
}
return det;
}
}

function cramersRule(matrix, freeTerms) {
// Switch to column major format
const n = matrix.length;
const matrixA = matrix
.reduce(
(acc, row) => {
row.forEach(
(elem, i) => acc[i].push(elem));
return acc;
},
Array(n).fill().map(_ => [])
);
// Compute original determinant
const detA = determinant(matrixA);
// Compute each solution value
const solution = [];
for (let i = 0; i < n; i++) {
const matrixAi = matrixA
.map((row, j) => j === i ? freeTerms : row);
const detAi = determinant(matrixAi);
solution.push(detAi / detA);
}
return solution;
}

console.log(cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49]));
``````