Matrices and Determinants

Matrix

Matrix- A matrix is a rectangular array of elements.

Rows- The horizontal arrangements are called rows.

Columns- The vertical arrangements are called columns.

Types of Matrices

The following are the different types of matrices

1. Row Matrix

2. Column Matrix

3. Square Matrix

4. Diagonal Matrix

5. Identity (or) Unit Matrix

6. Zero matrix (or) null matrix

7. Triangular Matrix

Algebraic Operations on Matrices

Basic operations on matrices are

(1) multiplication of a matrix by a scalar,

(2) addition/subtraction of two matrices, and

(3) multiplication of two matrices.

Properties of Matrix Addition, Scalar Multiplication and Product of Matrices

Symmetric and Skew-symmetric Matrices

Determinants

To every square matrix A = of order n, we can associate a number called determinant of the matrix A.

Product of Determinants

(i) Row by column multiplication rule

(ii) Row by row multiplication rule

(iii) Column by column multiplication rule

(iv) Column by row multiplication rule