Consider the following statements about the matrix M = pmatrix 71 &...

The given matrix is $M = \begin{pmatrix} 71 & 23 & 48 \\ 57 & 28 & 29 \\ 65 & 17 & 48 \end{pmatrix}$.

Let $C_1, C_2, C_3$ be the first, second, and third columns of the matrix $M$ respectively.

Observing the elements of the columns, we get:
$C_2 + C_3 = \begin{pmatrix} 23 + 48 \\ 28 + 29 \\ 17 + 48 \end{pmatrix} = \begin{pmatrix} 71 \\ 57 \\ 65 \end{pmatrix} = C_1$

Since the first column is the sum of the second and third columns, the columns of $M$ are linearly dependent.

Applying the column operation $C_1 \rightarrow C_1 - (C_2 + C_3)$, the first column becomes a zero column.

Therefore, the determinant of the matrix $M$ is $|M| = 0$.

Since the determinant is zero, $M$ is a singular matrix. Thus, the inverse of $M$ does not exist.

Statement-I is correct because the inverse of $M$ does not exist.

Statement-II is not correct because $M$ is a singular matrix.

Answer: Statement-I is correct but Statement-II is not correct