Use Cramer’s rule to solve for x, y and z
2x + y − 3z = 0
4x + 5y + z = 4
x + y − 4z = −1
First we find the coefficient determinant:
D= =-40-12+1+15-2+16=-22 .
Then we form and evaluate Dx by replacing the first column of values with the answer column:
Dx = = 0-12-1-15+0+16=-12.
Form and evaluate Dy by replacing the second column of values with the answer column:
Dy = = -32+12+0+12+2+0=-6 .
Form and evaluate Dz by replacing the third column of values with the answer column:
Dz = = -10+0+4-8+0+4=-10.
Cramer's rule says that x=Dx/D; y=Dy/D; z=Dz/D.
That is:
x=-12/-22=6/11; y=-6/-22=3/11; z=-10/-22=5/11.
The final answer:
(x,y,z)=(6/11, 3/11, 5/11) .
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