- #1

MathematicalPhysicist

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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?