Question

Evaluate the determinant of the matri [[7,2],[-4,-9]]

Answer 1

The determinant of the matrix [[7,2],[-4,-9]] is calculated using the formula ad - bc, resulting in a determinant of -55.

Step-by-step explanation:

To evaluate the determinant of the matrix [[7,2],[-4,-9]], we use the formula for the determinant of a 2x2 matrix: ad - bc, where a, b, c, and d are the elements of the matrix such that it can be represented as [[a, b], [c, d]].

The determinant of the given matrix is calculated as:

• a = 7
• b = 2
• c = -4
• d = -9

Applying the formula:

Determinant = ad - bc

Determinant = (7 * -9) - (2 * -4)

Determinant = -63 - (-8)

Determinant = -63 + 8

Determinant = -55

The determinant of the matrix is -55.