Find the determinant of the matrix \[\begin{bmatrix} 6 & -8 & 1 & 1\\ 0 & 2 & 4 & 6\\ 0 & 0 & 4 & 8\\ 0 & 0 & 0 & -1 \end{bmatrix}\]

Find the determinant of the matrix \[\begin{bmatrix} 6 & -8 & 1 & 1\\ 0 & 2 & 4 & 6\\ 0 & 0 & 4 & 8\\ 0 & 0 & 0 & -1 \end{bmatrix}\]. 

(A) 11, (B) -48, (C) 0, (D) -24

(GATE 1997)

Answer: (B) -48 

Explanation: 

The given matrix is an upper triangular matrix. 

We know that the determinant of an upper triangular matrix is the product of the main diagonal elements. 

Therefore, the determinant of the given matrix is $= 6 \times 2 \times 4 \times (-1) = -48$.  

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