a) Write the sequential version in C++ (refer the sequential algorithm below). Show the proof of correctness of your program (you can run your program with a small matrix size (e.g. 4x4 and small...

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Extracted text: a) Write the sequential version in C++ (refer the sequential algorithm below). Show the proof of correctness of your program (you can run your program with a small matrix size (e.g. 4x4 and small vector size (e.g. 4x1), verify it correctness, and attach a screenshot of correct result to this document). You can generate your matrix A and vector b using random numbers in the range of 1 to 10. Also, feel free to re-use any parts of the given codes to develop your own programs. Sequential Algorithm for matrix-vector multiplication a[0..m – 1,0..n – 1]– matrix with dimension m x n b[0..n – 1) – vector with dimension × 1 Input: Output: c0..m –- 1) – result vector with dimension m x 1 for i + 0 to m – 1 c[i] ++ 0 for j + 0 to n – 1 c[i) + c[t) + a[i, j) × b\j] endfor endfor b) Write MPI version in C++. Show proof of correctness.