Consider the following statements about the matrix M=\begin{bmatrix}71&23&48\\ 57&28&29\\ 65&17&48\end{bmatrix}: Statement-I: The inverse of M does <strong>NOT</strong> exist. Statement-II: M is non-singular. Which one of the following is correct in respect of the above statements?
- A. Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
- B. Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
- C. Statement-I is correct but Statement-II is not correct ✓
- D. Statement-I is not correct but Statement-II is correct
Correct Answer: C. Statement-I is correct but Statement-II is not correct
Explanation
Observe the columns of matrix M. The third column C_3 is the difference between the first and second columns (C_1 - C_2 = C_3 because 71-23=48, 57-28=29, 65-17=48). This linear dependency means \det(M) = 0. Therefore, M is singular and its inverse does not exist. Hence, Statement-I is correct and Statement-II is false.
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