Evaluate the determinant for the following matrix: [3 3 1} {-2 0 -2} {-2 4 -3}
a. -36
b. 12
c. 10
d. -42

Step-by-step

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

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.

good luck on ur quiz test or homework. have a good day : )