SOLUTION: My question is.... I was wondering how to do the cramer rule on a 3x3. I have found a bunch of examples and stuff, but I want to know how in the world do you find the determinants

Question 19634: My question is.... I was wondering how to do the cramer rule on a 3x3. I have found a bunch of examples and stuff, but I want to know how in the world do you find the determinants of the D, Dx, Dy.and Dz. If you could just tell me how, that would be great.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THE FOLLOWING AND COME BACK IF YOU HAVE DIFFICULTY.HERE C,CX,CY,CZ REFER TO YOUR D,DX,DY,DZ...JUST A DIFFERENCE IN NOMENCLATURE.I SHOWED IN DETAIL A 2X2 DETERMINANT AND THEN IN BRIEF A 3X3 DETERMINANT
2x+y=4
3x-y=6
make a deteminant with coefficients of x (2,3)and y(1,-1) in the 2 eqns.call it C.(Actually for a determinant as you know ,the numbers are contained in vertical bars at either end like |xx|,but in the following the bars are omitted due to difficulty in depiction.you may assume the bars are present)
C==2*(-1)-(1*3)=-5
..now use the constants (4,6)to replace coefficients of x(2,3) in the above determinant C...call it CX..
CX==4*(-1)-1*6=-4-6=-10
..now use the constants (4,6)to replace coefficients of y(1,-1) in the above determinant C...call it CY..
CY==2*6-3*4=12=12=0
..now cramers rule says that
..so we get
x/(-10)=y/0=1/-5
x=-10/-5=10/5=2
y=0/-5=0
************************************
so using the above method you can do the next problem ..here due to presence of 3 variables you will get 3rd.order determinants...4 in all...namely C,CX,CY and CZ,the last formula also extends to include z ,
..
but the procedure is same ..
2x+3y+ z= 5
x+y-2z= -2
-3x +z=-7 ...
...just to give you the idea
C=..and
CZ=..etc..hope you can work out the rest
RELATED QUESTIONS
I really don't know how to or do this stuff since our teacher makes use do it on the... (answered by jim_thompson5910)

So I am in AP calc this year, and I have to do a review test, and can't find any of my... (answered by jim_thompson5910)

Explain what outcomes of an experiment are. What does it mean to have equally likely... (answered by stanbon,jim_thompson5910)

Im sorry if this is in the wrong place, knew it went in either Polynomials or quadratic.... (answered by stanbon)

My Teacher has been of for ages and came in the other day to give us a homework sheet but (answered by nerdybill,richwmiller,solver91311)

How do you solve a 3x3 Matrix using Cramers rule. I know there is a way to do it by using (answered by ewatrrr)

I need a example of how to use the Cramer Rule step by... (answered by solver91311)

How do you do row reduction? I have no problem using elimination to find the values of... (answered by stanbon)

I have to solve this 4x4 matrix using Cramer's Rule: 4x + 0y + 3z - 2w = 2 3x + 1y + 2z (answered by venugopalramana,richwmiller)