C++ Programming: 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 five rows and six columns, we say that the matrix A is of the size 5 X 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 A = [aij] and B = [bij] and are two matrices of the same size m *n in which 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 are 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 is 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 = [c ik ] is of the size m t and the element cik is given by the formula: cik = ai1b1k + ai2b2k + ... + ainbnk 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 the matrices.
C++
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 five rows and six columns, we say that the matrix A is of the size 5 X 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 A = [aij] and B = [bij] and are two matrices of the same size m *n in which 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 are 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 is 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 = [c ik ] is of the size m t and the element cik is given by the formula:
cik = ai1b1k + ai2b2k + ... + ainbnk
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 the matrices.
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