Design a class to perform various matrix operations. A matrix is a set of numbers arranged in rows and columns. Therefore, every element of a matrix has a row position and a column position. If A is a matrix of 5 rows and 6 columns, we say that matrix A is of the size 5 × 6 and sometimes denote it as A 5×6 . Clearly, a convenient place to store a matrix is in a two-dimensional array. Two matrices can be added and subtracted if they have the same size. Suppose that A = [a, j] and
B = [bij ] are two matrices of the size m × n , where aij denotes the element of A in the i th row and the j th column, and so on. The sum and difference of A and B is given by
A + B [aij + bij ]; A − B [aij bij ]
The multiplication of A and B (A * B ) is defined only if the number of columns of A are the same as the number of rows of B . If A is of the size m × n and B is of the size n × t , then A * B = [cik ] is of the size m × t and the element cik is given by the formula
cik = ai 1 b 1k + ai 2 b 2 k + … + a in b nk
Design and implement a class matrixType that can store a matrix of any size. Overload the operators + , − , and * to perform the addition, subtraction, and multiplication operations, respectively, and overload the operator ≪ to output a matrix. Also, write a test program to test various operations on matrices.
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