Matrices and determinants Topics - IIT JEE Syllabus

1

2m1/10

📌 Key FormulaOrder of matrix: m × n, elements, notation A = [aᵢⱼ]

2

2m2/10

📌 Key FormulaAddition: (A + B)ᵢⱼ = aᵢⱼ + bᵢⱼ, Scalar multiplication: (kA)ᵢⱼ = k aᵢⱼ, Multiplication: (AB)ᵢⱼ = Σ aᵢₖ bₖⱼ

3

2m1/10

📌 Key FormulaRow, Column, Square, Diagonal, Scalar, Identity, Zero, Symmetric, Skew-symmetric

4

2m3/10

📌 Key Formuladet(A) = |A|, For 2×2 matrix [[a, b], [c, d]]: det = ad - bc. For 3×3 matrix: expansion along row/column.

5

2m4/10

📌 Key Formuladet(Aᵀ) = det(A), det(AB) = det(A) det(B), det(kA) = kⁿ det(A) for n×n matrix.

6

2m3/10

📌 Key FormulaExpansion by minors, row/column operations, factor theorem.

7

2m3/10

📌 Key FormulaArea = (1/2) |det([x₁, y₁, 1]; [x₂, y₂, 1]; [x₃, y₃, 1])|

8

2m4/10

📌 Key FormulaAdj(A) = Cᵀ (C is cofactor matrix), A⁻¹ = Adj(A) / det(A)

9

2m4/10

📌 Key FormulaCramer's rule, AX = B, solution exists if |A| ≠ 0, consistency using rank.