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Matrix Determinant
Matrix Determinant
Determinant with step-by-step reduction
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Matrix size
2 × 2
3 × 3
4 × 4
Matrix A
Reduce A to upper-triangular form by row operations, then det(A) = sign × (product of the diagonal pivots).
det(A)
-306
Sign
+1
Row swaps
0
Product of diagonal
6
· -2.666667
· 19.125
Row reduction
R2 → R2 − 0.666667·R1
R3 → R3 − 0.333333·R1
R3 → R3 − -2.875·R2
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Clear
A
6
1
1
4
-2
5
2
8
7
→
Upper-triangular form
6
1
1
0
-2.666667
4.333333
0
-0
19.125
det(A) = (
6
· -2.666667
· 19.125
) =
-306
