- Option : A
- Explanation : According to Rouche's theorem, the system is consistent if and only if the coefficient matrix and the augmented matrix K are of the same rank, otherwise the system is inconsistent.

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7. Rank of the diagonal matrix

- Option : D
- Explanation : Since the number of non-zero elements on this diagonal matrix is four, hence the rank is four.

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9. The matrix B = A^{T}, where A is any matrix is

- Option : C
- Explanation :

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10. Eigen values of a real symmetric matrix are always

- Option : D
- Explanation :

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