Applications of Matrices and Determinants — Revision Notes
Tamil Nadu Board · Class 12 · Mathematics
Applications of Matrices and Determinants revision notes for Tamil Nadu Board Class 12 Mathematics: 4 topics in quick points.
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Key Topics to Revise
1. Inverse of a Non-Singular Square Matrix
- A square matrix A is non-singular if |A| ≠ 0 (determinant is not zero)
- A square matrix A is singular if |A| = 0
- Adjoint of matrix A = Transpose of cofactor matrix
2. Elementary Transformations and Row-Echelon Form
- Three types of elementary row operations: (i) Interchanging rows, (ii) Multiplying row by non-zero scalar, (iii) Adding scalar multiple of one row to another
- Elementary column operations follow same rules but applied to columns
- Two matrices are equivalent (A ~ B) if one can be obtained from other by elementary transformations
3. Matrix Inversion Method for Solving Systems
- Applicable only when coefficient matrix A is square and non-singular (|A| ≠ 0)
- System AX = B has unique solution X = A⁻¹B
- Method involves: (1) Form coefficient matrix A, (2) Check |A| ≠ 0, (3) Find A⁻¹, (4) Multiply A⁻¹B to get X
4. Cramer's Rule
- Applicable when coefficient matrix is square and non-singular (|A| ≠ 0)
- Uses determinants to solve system: xᵢ = Δᵢ/Δ
- Δ = determinant of coefficient matrix
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