What is the determinant of cap d is equal to the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 3 row 2, column 1, negative 7 column 2, 6 ?

For a 2 by 2 matrix, the determinant is the product of the main diagonal entries minus the product of the other diagonal entries. Here, (-4 × 6) - (3 × -7) = -24 - (-21) = -3, so the determinant is negative 3.

AI-written and checked against the verified answer.