The basic arithmetic operations of addition, subtraction, multiplication and division can very well be performed on matrices subject to certain conditions and procedures lay down as under:
(i) Addition of Matrices
The matrices to be added to each other must be equivalent, i.e. each of the matrices must have equal number of rows, and equal number of columns, Symbolically, m1 = m3 and so on, and n1 = n2 and so on.
(a) Place all the matrices to be added in a horizontal lien and put + single between each of the pairs of them.
(b) Add the corresponding elements of each of the matrices and put their sums in the same order.
Subtraction of Matrices
Both the matrices i.e. the subtrahenal and the minuend matrices must be equivalent to each other. This means that each of the matrices must have equality in respect of the number of their rows and columns.
(a) Place both the matrices in a horizontal line put a – ve sign between the minuend and the subtrahenal matrices.
(b) Subtract the elements of the subtrahenal matrix from their corresponding elements in the minuend matrix and put their sums in the same order.
Multiplication of Matrices
There can be two types of multiplication with the matrices. They are:
(a) Scalar multiplication, and
(b) Multiplication proper.
These are explained here as under:
(a) Scalar Multiplication: When each element of a matrix is multiplied by a constant called a scalar, it is called scalar multiplication.
No condition as to the order of a matrix is necessary except that the scalar quantity must have been given.
(i) Write the scalar first, and then place the given matrix adjacent to it without putting any algebraic sign between them.
(ii) Multiply each element of the given matrix by the scalar given, and put the respective products in the same order.
Division of Matrices
The number of column in the divided matrix (n1) must be equal to the number of rows in the divisor matrix (m2).
Procedure. Proceed with the work of division just on the lines of multiplication proper explained above, explained above, except that each element in the dividend is to be multiplied by the reciprocal of the corresponding element of the divisor matrix (i.e. 1/e).