SOLUTION: which condition must be placed on a,b,c, so that the system x+2y-3z=a 2x+6y-11z=b x-2y+7z=c is consistent ? can the system have unique solution.

Question 1042313: which condition must be placed on a,b,c, so that the system
x+2y-3z=a
2x+6y-11z=b
x-2y+7z=c
is consistent ? can the system have unique solution.
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
which condition must be placed on a,b,c, so that the system
x+2y-3z=a
2x+6y-11z=b
x-2y+7z=c
is consistent ? can the system have unique solution.




-2R1+1R2->R2





-1R1+1R3->R3






2R2+1R3->R3





To be consistent, since all the elements
but the last one on the bottom row are 0,
the last one must be 0 also:







Or if you prefer c = 5a-2b

There will only be a unique solution if a=b=c=0

and that unique solution will be (x,y,z) = (0,0,0)

Edwin

RELATED QUESTIONS
Consider the system of equations x + 2y - 3z = a 2x + 6y - 11z = b x - 2y + 7z = c... (answered by MathLover1,math_tutor2020)

what condition a,b,c must staisfy so that the system x+y=2,y+z=2,x+z=2,ax+by+cz=0 is... (answered by ikleyn)

Consider the system x-2y+6z=a -x+y-z=b -3x+y+8z=c a)Determine the conditions (if... (answered by robertb)

Solve each system using the indicated method. State wheather the system is consistent or... (answered by jim_thompson5910)

2x − y = 5 4x − 2y = t (a) Determine a particular value of t so that the... (answered by ikleyn)

Let K be a real number. Consider the following system of equations: x - y + 3z =... (answered by ikleyn)

Given that (3, 2, �6) and (�2, 5, 1) are solutions of two equations in a system of three... (answered by Edwin McCravy)

I have been trying to solve these equations by graphing them but I'm getting a little... (answered by checkley75)

Please help with these difficult homework problems: 1. Find the intersection point of... (answered by robertb)