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The determinant distills a matrix to one number: scaling factor of the transformation, and the invertibility test (det = 0 → singular, no inverse). 2×2 and 3×3 via cofactor expansion.
2×2/3×3 determinant via cofactor expansion; singularity revealed.
2×2: ad−bc · 3×3: cofactor expansion along row 1
| Symbol | Meaning |
|---|---|
| det | Determinant (0 → singular) |
det[1,2;3,4] = 4−6 = −2 (invertible). det[1,2;2,4] = 0 (singular — rows dependent).
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Singular: the matrix squashes space flat — no inverse, and systems have 0/∞ solutions.
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Content updated: September 2026