lightbulb Key Concepts

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1. Definition

A determinant is a number associated with a square matrix. For a 2×2 matrix |a b; c d|, the determinant is ad - bc.

2. Minors and Cofactors

• Minor (Mᵢⱼ): Determinant of the sub-matrix after deleting i-th row and j-th column.
• Cofactor (Aᵢⱼ): (-1)ⁱ⁺ʲ · Mᵢⱼ.

3. Properties of Determinants

• |AB| = |A| |B|
• If any two rows (or columns) are identical, the determinant is 0.
• Multiplying a row by k multiplies the determinant by k.