I have trouble solving the following question: Question
How I approached it initially was as follow:
1) Since the questions asks for x3 only, I replaced the x3 column with the particular solution. Step 1
2) Cramer's Rule asks of us to divide the det(Substituted Matrix in Step 1) by the det(Initial Matrix) Step 2
3) To find the det of each 4x4 matrix I did C(1,1)(det(3x3 sub Matrix)). So 1(det(3x3 sub Matrix)). I evaluated the 3x3 sub Matrix as follow: 3x3 sub Matrix The red arrows are added and then subtracted to the addition of the blue arrows. Thus det(Substituted Matrix) = 3aei + 3bfg + 2cdh - 3ceg - 2afh - 3bdi.
4) I did step 3 for the initial Matrix as well and got det(Initial Matrix) = aei + bfg + cdh - ceg - afh - bdi
Now, I am unsure how to work around the determinants I just got. I should factor out something and then cancel the rest, but I don't see what. Did I miss something?