Binomial theorem Topics - IIT JEE Syllabus

1

2m4/10

📌 Key FormulaFinding remainder, approximations, expansions.

2

2m1/10

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

3

2m1/10

📌 Key FormulaTwo matrices are equal if same order and corresponding elements equal.

4

2m2/10

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

5

2m2/10

📌 Key FormulaAs above.

6

2m1/10

📌 Key Formula(Aᵀ)ᵢⱼ = aⱼᵢ

7

2m2/10

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

8

2m3/10

📌 Key FormulaA⁻¹ = Adj(A) / det(A), defined only if det(A) ≠ 0.

9

2m1/10

📌 Key FormulaNon-diagonal elements are zero.

10

2m1/10

📌 Key FormulaAᵀ = A

11

2m1/10

📌 Key FormulaAᵀ = -A

12

2m4/10

📌 Key FormulaUsing matrix inversion (AX = B → X = A⁻¹B) or Cramer's rule.