A Note In this chapter . We shall follow the notation, namely A = [ a ij ] m × n to indicate that A is a matrix of order m × n . . We shall consider only those matrices whose elements are real numbers or functions taking real values.
We can also represent any point ( x , y ) in a plane by a matrix (column or row) as (or [ x , y ]). For example point P( , ) as a matrix representation may be given as P = or [ ]. Observe that in this way we can also express the vertices of a closed rectilinear figure in the form of a matrix. For example, consider a quadrilateral ABCD with vertices A ( , ), B ( , ), C ( , ), D (– , ).
Now, quadrilateral ABCD in the matrix form, can be represented as C D X A Y C D − Thus, matrices can be used as representation of vertices of geometrical figures in a plane. Now, let us consider some examples. Example Consider the following information regarding the number of men and women workers in three factories I, II and III Men workers Women workers I II III Represent the above information in the form of a × matrix. What does the entry in the third row and second column represent?
Solution The information is represented in the form of a × matrix as follows: The entry in the third row and second column represents the number of women workers in factory III. Example If a matrix has elements, what are the possible orders it can have? Solution We know that if a matrix is of order m × n , it has mn elements. Thus, to find all possible orders of a matrix with elements, we will find all ordered pairs of natural numbers, whose product is .