- #1
yango_17
- 60
- 1
Homework Statement
Find all solutions of the linear system
x + 2y + 3z = a
x + 3y + 8z = b
x + 2y + 2z = c
where a,b, and c are arbitrary constants.
Homework Equations
The Attempt at a Solution
Using elimination, I managed to set the coefficients on the diagonal equal to 1, which then allowed me to solve for z, which was z = -c + a. Substituting z into the other equations to obtain x and y, I ended up with the following solution:
x= -6a - 2b + 13c
y = b + 4a -5c
z = a - c
I was wondering if my method of solving is valid, and if the answer I obtained seems reasonable. Thanks.