Consider the following statements about the matrix M= bmatrix 71&23&48 57&28&29 65&17&48 bmatrix : Statement-I : The inverse of M does not exist. Statement-II : M is non-singular. Which one of the following is correct in respect of the above statements?

NDA 2025 Mathematics question

Consider the following statements about the matrix : Statement-I : The inverse of does not exist. Statement-II : 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 correctCorrect
(D)Statement-I is not correct but Statement-II is correct

Answer: (C)

Solution

In every row the first entry is the sum of the other two: , , . So , the columns are linearly dependent

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Question ID VK-030176