Evaluate the determinant for the following matrix: [3 3 1} {-2 0 - 2} {-2 4 - 3}

A. - 36

B. 12

C. 10

D. - 42

10

Step-by-step explanation:

Separate the top row:

3 3 1

Make sure they are alternating in sign starting with +, then-, then +:

+3 - 3 + 1

Now next to each of the we will be multiplying it by the determinant of the matrix that contain the elements not directly under these number in the given matrix:

+3[ 0 - 2] - 3[-2 - 2] + 1[-2 0]

[4 - 3] [-2 - 3] [-2 4]

Now to find the determinant of each 2 by 2:

3 (0*-3 - (-2) * 4) - 3 (-2 (-3) - (-2) (-2)) + 1 (-2 (4) - 0 (-2))

3 (0+8) - 3 (6-4) + 1 (-8-0)

3 (8) - 3 (2) + 1 (-8)

24-6-8

24-14

10

So the determinant is 10.

You can use some calculators to check this answer.

Step-by-step answer:

determinant of

3 3 1

-2 0 - 2

-2 4 - 3

expand by second row, note the sign of cofactors

-[-2 (3 * (-3) - 4*1) ] + [0 (3*3 - (-2*1)) ] - [-2 (3*4 - (-2*3)) ]

=2 (-13) + 0 + 2 (18)

=-26+0+36

=10