The determinant should be 4.
So I have the matrix
1 0 1 0
0 1 0 1
-2 1 1 0
0 0 1 1
I chose row 3 column 2 and will take it's minor. The minor is
1 1 0
0 0 1
0 1 1
Row two has the most zeros, and so I will select row 2. This leaves me to calculate only row 2 column 3. Which is
If I'm not mistaken, the determinant should be 1.
From the 4x4 matrix I have (-1)^3+2 * 1 = 1
From the 3x3 I have only (-1)^2+3 * 1 = 1
All of this just ends up as 1. Am I correct?
You just forgot to compute some steps...you still have to go back to your original matrix and repeat the same process.
I decided to choose the first row for the first step instead of the 2nd row like you chose cause the first row has the most zeros. I just wrote it by hand cause ... well, it was simpler that way. Tell me if this makes sense!
(Also, those should be -1's, not 1's, although it doesn't make a difference cause they are raised to even powers and become even anyway)
Strictly speaking there would two more minors but they would be multiplied by the "0"s in those positions.
To evaluate those two determinants, expand the first one on the last column:
Expand the second on the second row:
The reason for the choice of the last column and second row was that there was only one non-zero entry so we needed only one minor.
The original determinant is 3- (-1)= 4.