Question

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

A. -36
B. 12
C. 10
D. -42

Answer 1

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

Answer 2

10

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.