Prove the following corollary to the Rank Theorem: Let A be an m x n matrix with entries in Z. Any consistent system of linear equations with coefficient matrix A has exactly on rank(A) solutions over Zo Quantify how many solutions are associated with each free variable. Compute the total number of solutions over R. Identify the total number of solutions. Take the total number of solutions over R modulo p. Construct an example and count the number of solutions. Chose from the statements above to form an outline to the proof. 1. Use the Rank Theorem to identify the number of free variables. 2. Quantify how many solutions are associated with each free variable. 3. Identify the total number of solutions. Using the outline above, write the complete proof. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen Prove the following corollary to the Rank Theorem: Let A be an m x n matrix with entries in Z. Any consistent system of linear equations with coefficient matrix A has exactly on rank(A) solutions over Zo Quantify how many solutions are associated with each free variable. Compute the total number of solutions over R. Identify the total number of solutions. Take the total number of solutions over R modulo p. Construct an example and count the number of solutions. Chose from the statements above to form an outline to the proof. 1. Use the Rank Theorem to identify the number of free variables. 2. Quantify how many solutions are associated with each free variable. 3. Identify the total number of solutions. Using the outline above, write the complete proof. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen