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Charismaztex
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Homework Statement
1) Determine, by elimination, value of a (if any) such that the given system will have a unique solution
[itex]x+2y+3z=2,
2x+2y+az=0,
3x+2y+z=0[/itex]
2) Determine, by elimination, values of a (if any) such that the given system:
a) Is consistent with and infinity of solutions;
b) has a unique solution;
c) is inconsistent, with no solution
[itex]x+2y+3z=a,
x+y+z=0,
3x+2y+z=0[/itex]
3) consider the following system of 3 equations in x,y, and z
[itex] 2x+2y+2z=9,
x+3y+4z=5,
Ax+5y+6z=B[/itex]
Give possibly values of A and B in the third equation which make this system:
a) inconsistent
b) consistent but with an infinite number of solutions
Homework Equations
N/A
The Attempt at a Solution
1) By a unique solution I'm presuming that all three planes meet at the same point. Would this be to solve and get a so that x,y, and z have a unique value?
2) Consistent with infinity of solutions, is that when we get a situation 0=0? Possibly with at least 2 of the plane equations the same, or intersecting like the "spine" of a book. So a value of a to get some sort of 0=0?
would inconsistent be a situation when we get 0=a number (a nonsense statement)?
To be honest, I have no idea how to approach the question which as to determine values of a or A and B. What sort of method would be suitable?
Thanks in advance,
Charismaztex