The determinant of the matrix is

The correct answer is: 4.

From the image, the matrix is:

[ 2  0  0  0 ]
[ 8  1  7  2 ]
[ 2  0  2  0 ]
[ 9  0  5  1 ]

Expand the determinant along the first row. Since the only non-zero entry in the first row is 2, we get:

det(A) = 2 × det([ [1, 7, 2], [0, 2, 0], [0, 5, 1] ]).

Now compute the 3 × 3 determinant:

det([ [1, 7, 2], [0, 2, 0], [0, 5, 1] ]) = 1(2 × 1 - 0 × 5) = 2.

Therefore:

det(A) = 2 × 2 = 4.