- #1
MathematicalPhysicist
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we have the system a_i1x+a_i2y+a_i3z=b_i i=1,2,3
and we are given that it has a unique solution (1,2,0)
i need to find the set of solutions for the next system:
a_i1x+b_iy+a_i3z=a_i2
what i did is:
we have the solution for the first equation then we have a_i1+2a_i2=b_i
so we put it in the second equation and we have:
a_i1x+(a_i1+2a_i2)y+a_i3z=a_i2
(a_i1x+a_i2y+a_i3z)+(a_i1+a_i2)y=a_i2
b_i+(a_i1+a_i2)y=a_i2
(a_i1+2a_i2)+(a_i1+a_i2)y=a_i2
from here i found the solution, is this method valid?
and we are given that it has a unique solution (1,2,0)
i need to find the set of solutions for the next system:
a_i1x+b_iy+a_i3z=a_i2
what i did is:
we have the solution for the first equation then we have a_i1+2a_i2=b_i
so we put it in the second equation and we have:
a_i1x+(a_i1+2a_i2)y+a_i3z=a_i2
(a_i1x+a_i2y+a_i3z)+(a_i1+a_i2)y=a_i2
b_i+(a_i1+a_i2)y=a_i2
(a_i1+2a_i2)+(a_i1+a_i2)y=a_i2
from here i found the solution, is this method valid?