- #1
thecokeguy
- 7
- 0
Homework Statement
I have the following system og equations:
[itex]
\left\{\begin{array}{l}
y + 2z = 1 \\
x + 4y + 3z = C \\
x + y + Bz = B
\end{array}\right.
[/itex]
a) Create the augmented matrix and reduce to row echelon form (I've already done this)
b) For which values of A and B is the system inconsistent?
c) For which values of A and B does the system have only one solution?
d) Determine the complete solution to the system for all values of A and B.
Homework Equations
The system in row echelon form:
[itex]
\begin{pmatrix}
1 & 4 & 3 & C \\
0 & 1 & 2 & 1 \\
0 & 0 & 1 & \frac{B - C + 3}{B + 3}
\end{pmatrix}
[/itex]
The Attempt at a Solution
Earlier when solving this kind of problems with systems with 2 variables, I solved it geometrically as lines being parallel, intersecting etc. Of course this could be solved geometrically too as planes, but as I can't imagine how to do it geometrically with >3 variables, I thought I've missed something.
If someone could point me in a direction, then I'll figure out the rest myself.
Thanks.