MATRICES
Introduction | Concept, Notation and order. |
Types of matrices | Column matrix, row matrix, rectangular matrix, square matrix, zero matrix, diagonal matrix, scalar matrix and unit matrix. |
Algebra of matrices | Equality of matrices, Addition, multiplication, scalar multiplication of matrices, Transpose of a matrix. Mentioning properties with respect to addition, multiplication, scalar multiplication and transpose of matrices. |
Symmetric and Skew Symmetric matrices | Definitions |
Properties of symmetric and skew symmetric matrices: | Proofs of |
i) If a is any square matrix a+a′ is symmetric and a-a′ is skew symmetric. | |
ii) Any square matrix can be expressed as the sum of a symmetric and a skew symmetric matrix. | |
Concept of elementary row and column operations | Finding inverse of a matrix restricted to 2×2 matrices only. |
Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |