Question: The purpose of this project is to provide practice with matrix multiplication and the reduction of matrices to their row-reduced echelon forms using computer algebra
1. If A, B, and C are arbitrary rectangular matrices, it can be shown that when the matrix product ABC exists, then
Rank(AB) + Rank(BC) ≤ Rank(B) + Rank(ABC)
2. Define three arbitrary rectangular matrices A, B, and C for which the product ABC is defined. Using computer algebra matrix multiplication and computer algebra row-reduction to echelon form, find the ranks of AB, BC, B, and ABC, and hence confirm the inequality in Step 1 for this particular case.