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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

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B

Rank A = Rank of C = r, r < n, Infinite solutions

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C

Rank A = Rank of C = n, unique solution

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D

Rank A = Rank of C = r< n, unique solution

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Solution

The correct options are
B

Rank A = Rank of C = r, r < n, Infinite solutions


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.


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