Question

Evaluate the determinate of the matrix with work shown.

Answer 1

1. Divide the first row by -4

(1, -5/4, -3/2)

2. Multiply the first row by -2

(-2, 5/2, 3)

3. Subtract the first row from the third row and restore it.

1 (1, -5/4, -3/2)

3 (0, -15/2, 1)

4. Restore the first row to the original view

(-4, 5, 6)

5. Divide the second row by 4

(0, 1, 1)

6. Multiply the second row by -15/2

(0, -15/2, -15/2)

7. Subtract the second row from the third row and restore it

2 (0, 1, 1)

3 (0, 0, 17/2)

8. Restore the second row to the original view

(0, 4, 4)

9. Multiply the main diagonal elements

-4 x 4 x 17/2 = 136

Answer: Δ = 136