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Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29 65 & 17 & 48 pmatrix : 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?

Options

  1. ABoth Statement-I and Statement-II are correct and Statement-II explains Statement-I
  2. BBoth Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
  3. CStatement-I is correct but Statement-II is not correct
  4. DStatement-I is not correct but Statement-II is correct

Correct answer

C. Statement-I is correct but Statement-II is not correct

Step-by-step solution

The given matrix is M = pmatrix 71 & 23 & 48 57 & 28 & 29 65 & 17 & 48 pmatrix . Let C₁, C₂, C₃ be the first, second, and third columns of the matrix M respectively. Observing the elements of the columns, we get: C₂ + C₃ = pmatrix 23 + 48 28 + 29 17 + 48 pmatrix = pmatrix 71 57 65 pmatrix = C₁ Since the first column is the sum of the second and third columns, the columns of M are linearly dependent. Applying the column operation C₁ C₁ - (C₂ + C₃) , the first column becomes a zero column. Therefore, the determinant

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