a. Show that for every n x m matrix A with rank( A) < n, there exists a vector b in R" such that the system A = b is inconsistent. Hint: Consider an n x m matrix A. For E = rref( A), show that there exists a vector c in R" such that the system Er = c is inconsistent; then, "work backward." b. Show that for every n x m matrix A with n > m, there exists a vector b in R" such that the system A = b is inconsistent.

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