d3bugg3r
asked on
gauss elimination with parameters
I'm breaking my head trying to figure out what i'm doing wrong,
i'm support to eliminate the following equations using Gauss elimination system
ax+y+z=4
x+by+z=3
x+2by+z=4
and i'm suppose to figure out for which a,b (which are Parameters) the system has One solution/Infinit Solutions/No solutions - if there's infint solutions i'm suppose to write the general solution for the system.
now it's all pretty basic in the begining
1 b 1 3
1 2b 1 4 R2->R2-R1
a 1 1 4 R3->R3-aR1
which leads me to
1 b 1 3
0 b 0 1 * i can reach the first value using /:b , i then get y=1/b
0 1-ab 1-a 4-3a
from here i'm puzzled as there's no way to carry on the elimination (if i'm doing it right)
i'm support to eliminate the following equations using Gauss elimination system
ax+y+z=4
x+by+z=3
x+2by+z=4
and i'm suppose to figure out for which a,b (which are Parameters) the system has One solution/Infinit Solutions/No solutions - if there's infint solutions i'm suppose to write the general solution for the system.
now it's all pretty basic in the begining
1 b 1 3
1 2b 1 4 R2->R2-R1
a 1 1 4 R3->R3-aR1
which leads me to
1 b 1 3
0 b 0 1 * i can reach the first value using /:b , i then get y=1/b
0 1-ab 1-a 4-3a
from here i'm puzzled as there's no way to carry on the elimination (if i'm doing it right)
ASKER
I dont see how it's possible, it will give the following result for the 3rs equation:
0 0 0 0 1 which is not possible, not as a solution anyway.
0 0 0 0 1 which is not possible, not as a solution anyway.
What happens to the 1st and 2nd equations if a = b = 1 ??
You don't have to solve them, just look at them.
You don't have to solve them, just look at them.
ASKER
yes, it works out... but it doesnt for the 3rd so i cannot use those values as answer.
and i have to define if for those two parameters there's uniqe solution, unlimited solutions or no solutions (like if b=0 then 1/0 on the second equation isnt possible)
and i have to define if for those two parameters there's uniqe solution, unlimited solutions or no solutions (like if b=0 then 1/0 on the second equation isnt possible)
ASKER CERTIFIED SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
What happens if a = b = 1 ??
What values will make the 1st and 3rd equations wierd??