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Matrices are the plural form of matrix. A matrix is a rectangular array numbers arranged in rows and columns. If m x n numbers are arranged in a rectangular array of m rows and n columns, it is called, it is called a matrix of m by n or a matrix of dimension m x n or a matrix of type m x n.

Types of matrices: -

·         Rectangular matrix
·         Square matrix
·         Row and column matrix
·         Null matrix or zero matrix
·         Diagonal matrix and unit or identity matrix
·         Equality of matrices
·         Singular and non- singular matrices
·         Transpose of a matrix
·         Symmetric and skew-symmetric matrices
·         Co-efficient matrix and augmented matrix

Operations of matrices

·         Scalar multiplication of a matrix
·         Addition and subtraction of matrices
·         Multiplication of matrices.

Let’s discuss the addition of matrices.

The addition of two matrices A and B is defined if and only if they are of the same order. If A and B are two matrices each of order m x n , then their sum A + B is also a matrix of order m x n, whose elements are obtained by adding the corresponding elements of A and B.

Example1: -   If A = |1  3|         and B= |6       5|
|2   4|                       |8       7|
Find A + B.

Solution: -
A + B= |1+6   3+5|    =|7       8|
|2+8   4+7|      |10  11|

Example2: - Find
|2         4          -3| + |-7           3          6|
|6         5          1|     | -2         1          5|

Solution: -  |2+ (-7)   4+3     -3+6| =|-5       7          3|
|6+ (-2)    5+1     1+5 |   |4         6          6|