Hi I ran across this problem and could not figure it out. Could someone please give me an explanation? I feel like I have something close but no cigar.
Compute the following determinants by using row and/or column reduction
Then, I applied the following row operations.
R2->R2+2R3
R3->3R3-2R1
Here's where it goes wrong. When you multiply R3 by 3 you multiply the determinant by 3. That's why you end up with 3 times the correct answer.
I also factored out the 3 from the top row.
3
Then, R3->R3-33/9R2
3
Det=3*1*9*-107/3=-963
However, the answer should be -321.