(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

N/A

3. 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Questions on 3 simultaneous equations (3D vector planes)

**Physics Forums | Science Articles, Homework Help, Discussion**