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Question 18759: I have to solve this 4x4 matrix using Cramer's Rule:
4x + 0y + 3z - 2w = 2
3x + 1y + 2z - 1w = 4
1x - 6y - 2z + 2w = 0
2x + 2y + 0z - 1w = 1
Once I get to finding the determinants of the three 3x3 matrices, I am completly lost. Do you solve like a normal 3x3 and just multiply the determinent found by the number on the outside? After that is it simply repeating the same process for the other variables and adding the answers together?
Found 2 solutions by venugopalramana, richwmiller:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! UNFORTUNATELY THAT IS THE CRAMER'S RULE.SINCE THE QUESTION IS TO BE SOLVED BY USING CRAMER'S RULE THERE IS NO OTHER WAY.YOU WILL HAVE TO FIND VALUES OF FOURTH ORDER DETERMINANTS,BY SUCCESSIVELY REDUCING THEM TO THIRD ORDER ,THEN SECOND ORDER AND FINALLY FIRST ORDER.BUT GENERALLY EASIER NUMBERS ARE GIVEN WITH ZEROS ONES ETC.TO MAKE WORKING EASIER.THERE ARE OTHER BETTER METHODS ,BUT AS PER THE REQUREMENT THEY CANNOT BE USED HERE.IF YOU NEED FURTHER HELP COME BACK
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! 4,0,3,-2,2
3,1,2,-1,4
1,-6,-2,2,0
2,2,0,-1,1
D=39
Dx=52
Dy=39
Dz=52
Dw=143
x=Dx/D= 52/39 = 1.33333333
y=Dy/D= 39/39 = 1
z=Dz/D= 52/39 = 1.33333333
w=Dw/D= 143/39 = 3.66666667
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