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 unknownsA- Rank A - Rank of C - n- Infinite solutionsB- Rank A - Rank of C - r - r - n- Infinite solutionsC- Rank A - Rank of C-n- unique solutionD- Rank A - Rank of C - r - n- unique solution

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Rank of a Matrix

Which of the ...

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

Rank A = Rank of C=n, Infinite solutions

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

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Rank A = Rank of C = n, unique solution

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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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