Question 389305: use Cramer's rule :
3x+2y-z=0
2x-1y+3z=-1
-2x+2z=4
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 3x+2y-z=0_2x-1y+3z=-1_-2x+2z=4
Move all terms containing variables to the left-hand side of the equation.
3x+2y-z=0_2x-y+3z=-1_-2x+2z=4
Represent the system of equations in matrix format.
M[3,2,-1:2,-1,3:-2,0,2]M[x:y:z]=M[0:-1:4]
Setup the determinant by breaking it into smaller components.
D=-(2)M[D,2,3:-2,2]-1M[D,3,-1:-2,2]+0M[D,3,-1:2,3]
The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
D=-(2)((2)(2)-(-2)(3))-1M[D,3,-1:-2,2]+0M[D,3,-1:2,3]
Simplify the expression.
D=-24
Setup the determinant by breaking it into smaller components.
Dx=0M[D,-1,3:0,2]-(-1)M[D,2,-1:0,2]+4M[D,2,-1:-1,3]
Since the matrix is multiplied by 0, the determinant is 0.
Dx=0-(-1)M[D,2,-1:0,2]+4M[D,2,-1:-1,3]
Simplify the expression.
Dx=24
Setup the determinant by breaking it into smaller components.
Dy=0M[D,2,3:-2,2]-1M[D,3,-1:-2,2]-(4)M[D,3,-1:2,3]
Since the matrix is multiplied by 0, the determinant is 0.
Dy=0-1M[D,3,-1:-2,2]-(4)M[D,3,-1:2,3]
Simplify the expression.
Dy=-48
Setup the determinant by breaking it into smaller components.
Dz=-(2)M[D,2,-1:-2,4]-1M[D,3,0:-2,4]+0M[D,3,0:2,-1]
The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
Dz=-(2)((2)(4)-(-2)(-1))-1M[D,3,0:-2,4]+0M[D,3,0:2,-1]
Simplify the expression.
Dz=-24
Find the value of x by Cramer's Rule, which states that x=(Dx)/(D).
x=(24)/(-24)
Move the minus sign in the denominator to the front of the expression.
x=-(24)/(24)
Reduce the expression -(24)/(24) by removing a factor of 24 from the numerator and denominator.
x=-1
Find the value of y by Cramer's Rule, which states that y=(Dy)/(D).
y=-(48)/(-24)
Since the numerator and denominator are both negative, remove the minus sign from each.
y=(48)/(24)
Reduce the expression (48)/(24) by removing a factor of 24 from the numerator and denominator.
y=2
Find the value of z by Cramer's Rule, which states that z=(Dz)/(D).
z=-(24)/(-24)
Since the numerator and denominator are both negative, remove the minus sign from each.
z=(24)/(24)
Reduce the expression (24)/(24) by removing a factor of 24 from the numerator and denominator.
z=1
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