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:
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.
