Question 1571
 Adding the 2nd row to the first row, we have

   2 4  0  0
   1 2  1  2 
   1 0  0  1
   0 1  1  0

 Adding the 1st row times -1/2 row to the 2nd row, we have
   2 4  0  0
   0 0  1  2 
   1 0  0  1
   0 1  1  0
 
 to find the determinant by expanding along the 1st column, we have
   |0  1  2|      |4  0  0|
  2|0  0  1| +    |0  1  2|
   |1  1  0|      |1  1  0|
 
   = 2 +  4(-2) = -6.