Question

Which of the following is true if A and C are coefficient and augmented matrices respectively for a system of linear equation. Here n = number of unknowns

• A. Rank A = Rank of C=n, Infinite solutions
• B. Rank A = Rank of C = r, r < n, Infinite solutions
• C. Rank A = Rank of C = n, unique solution
• D. Rank A = Rank of C = r< n, unique solution

Answer 1

Answer: (B), (C)

Rank A = Rank of C = n, unique solution

The given equations are consistent only when Rank of A = Rank of C.

When Rank of A = Rank of C = n.

Then there exists only a unique solution.

When Rank of A = Rank of C = r < n

Then there exists infinite solution.

Therefore b and c are correct.