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The determinant of a square matrix encodes whether it's invertible (det≠0), the volume scaling of the linear transformation, and orientation change. det=0 → singular matrix.
Steg-för-steg-guide
- 12×2: det [[a,b],[c,d]] = ad − bc
- 23×3: cofactor expansion along first row
- 3det<0 → transformation reverses orientation
Lösta exempel
Ingång
2×2 matrix [[a,b],[c,d]]
Resultat
det = ad − bc
For [[3,1],[2,4]]: det = 12−2 = 10
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