Class 12 Maths Chapter 4: Determinants – Properties, NCERT Solutions & CBSE PYQs
Here’s your comprehensive guide for Chapter 4: Determinants (Class 12 CBSE Maths), covering: 🧠A. Key Concepts & Properties 1. What Is a Determinant? Assigns a scalar value to a square matrix. For 1 × 1 1 \times 1 : ∣ [ a ] ∣ = a |[a]| = a ; For 2 × 2 2 \times 2 , ∣ a b c d ∣ = a d − b c \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc ; For 3 × 3 3 \times 3 , use expansion by minors and cofactors. 2. Properties of Determinants (Useful for simplifying evaluations) : Transpose Invariance : ∣ A ∣ = ∣ A T ∣ |A| = |A^T| Sign Swap : Swapping two rows flips the sign Zero/Equal Row : Any row (or column) of zeros or two identical rows ⇒ ∣ A ∣ = 0 |A| = 0 Scalar Factor : Multiplying a row by k k scales ∣ A ∣ |A| by k k Linearity : Split row entries into sums to split determinant Triangular Matrix : Determinant equals product of diagonal entries 3. Minors, Cofactors & Expansion Minor M i j M_{ij} : Determinant obt...