Section 17

Determinants and inverses

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det (a c b d) = a d - b c

Oriented area scaling factor in 2D.

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det (A) = j \sum a_{ij} C_{ij}

Expands a determinant along a row or column.

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det (A B) = det (A) det (B)

The overall scaling factor multiplies under composition.

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A invertible ⟺ det (A) \neq = 0

Characterizes invertible square matrices.

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A^{- 1} = \frac{1}{a d - b c} (d - c - b a)

Inverts a nonsingular 2×2 matrix.

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x_{i} = \frac{det ( A _{i} )}{det ( A )}

Solves nonsingular square systems using determinants.