Design a class to perform various matrix operations. A matrix is a set of numbers arranged in rows and columns?

Question

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 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 x 6 and sometimes denote it as A 5x6. 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 = [aij] and B = [bij] are two matrices of the size m x n, where aij denotes the element of A
in the ith row and the jth column, and so on. The sum and difference of A and is given y
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 x n and B is of the size n x t then A * B = [cik] is of the size m x t and the
element cik is given by the formula
cik = ai1bi1 + ai2bi2 + ... + ainbin
Design and implement a class matrixType that can store a matrix of any size. Overload the operator +,-, and *
to perform the addition, subtraction, and multiplication operations, respectively, and overload the operator
<< to output a matrix. Write a test program to test various operations on matrices

Answer 1

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Answer 2

regrettably, matrix algebra is one in all those challenging instructions in lots of circumstances reserved for engineers and math majors. the forged information is that mutually as you will possibly not understand matrices, gaining expertise of the elementary operations isn't too terriblly complicated. curiously, the operation you describe does exist and is named "dot-matrix multiplication." In dot-matrix multiplication: A = [a1 a2] B = [b1 b2] A * B = [a1 a2] * [b1 b2] = [a1*b1 a2*b2] notice which you will unlikely bump into the type of operation quickly, as that's uncommon until eventually you attain intermediate college courses. once you paintings with matrices, it rather is significant to bear in mind that they are typical to characterize vectors (parts that require the two a magnitude and a direction--ex: velocity can in basic terms be quantified with the two a velocity and a direction). long tale short, the classic approach of matrix multiplication has important implications in larger point arithmetic. a achievable occasion you will be able to appreciate is an identity matrix. bear in mind that in the time of multiplication, a type circumstances a million yields the unique type. further, any matrix could be elevated by its suited identity matrix and the product may be the unique matrix. (3-by-3) identity matrix: a million 0 0 0 a million 0 0 0 a million notice that any matrix could be got here upon to be the fabricated from itself and an (accurately sized) identity matrix. in truth, you will ought to settle for which you will not understand why matrices are elevated this way. besides the undeniable fact that, take convenience in understanding that there is a reason of the insanity.

Answer 3

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