Matrices - Defination, Notes 

What is Matrice?

Matrices are rectangular grids of numbers or symbols used to organize and manipulate data. They find applications in mathematics, physics, computer science, and engineering. Matrices can be added, subtracted, and multiplied, and they allow for operations like transposition. They are crucial for solving systems of linear equations, performing transformations, and analyzing data in statistics. Matrices play a fundamental role in linear algebra, calculus, and differential equations. They provide a versatile tool for organizing data, making calculations, and solving complex problems in various fields.

 

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Table of Content 

1. Definition.

2. Order of a matrix.

3. Equality of matrices.

4. Types of matrices.

5. Addition and subtraction of matrices.

6. Scalar multiplication of matrices.

7. Multiplication of matrices.

8. Positive integral powers of a matrix.

9. Matrix polynomial.

10. Transpose of a matrix.

11. determinants of a matrix.

12. Special types of matrices.

13. Adjoint of a square matrix.

14. Inverse of a matrix.

15. Elementary transformation or Elementary operations of a matrix.

16. Elementary matrix.

17. Rank of matrix.

18. Echelon form of a matrix. 

19. System of simultaneous linear equations.

20. Solution of a non-homogeneous system of linear equations.

21. Cayley-Hamilton theorem.

22. Geometrical transformations.

23. Matrices of rotations of axes