Lesson 4.7: Matrices & Determinants

Matrices and Determinants are important topics in the Mathematics section for NDA, CDS, and AFCAT exams. They help aspirants solve linear equations, algebraic problems, and numerical analysis efficiently.

1. Basics of Matrices

• Definition: A matrix is a rectangular array of numbers arranged in rows and columns.

• Notation: A = [aᵢⱼ] where i = row, j = column

• Types of Matrices:

  • Row matrix, Column matrix, Square matrix

  • Diagonal, Scalar, Identity, Zero matrix

• Operations: Addition, Subtraction, Scalar Multiplication

2. Determinants

• Definition: A determinant is a scalar value derived from a square matrix.

• 2×2 Matrix Determinant:

  • For A = [abcd]\begin{bmatrix}a & b\\ c & d\end{bmatrix}[ac​bd​], det(A) = ad – bc

• 3×3 Matrix Determinant: Use expansion method or Sarrus’ Rule

• Properties of Determinants:

  • det(Aᵀ) = det(A)

  • Multiplying a row by a constant multiplies determinant by the same constant

  • Determinant of identity matrix = 1

3. Applications

• Solving simultaneous linear equations using Cramer’s Rule

• Evaluating area of triangles in coordinate geometry

• Checking invertibility of matrices

Exam Tips

• Memorize basic formulas and properties of matrices and determinants.

• Practice solving 2×2 and 3×3 determinant problems.

• Solve previous year NDA, CDS, AFCAT questions on matrices.

• Focus on step-by-step calculations to avoid errors.