SOLUTION: Consider the following subspace of R^3: W={(x,y,z)belong to R^3|2x+2y+z=0, 3x+3y-2z=0,x+y-3z=0} The dimension of W is

Algebra ->  College  -> Linear Algebra -> SOLUTION: Consider the following subspace of R^3: W={(x,y,z)belong to R^3|2x+2y+z=0, 3x+3y-2z=0,x+y-3z=0} The dimension of W is       Log On


   

Question 893904: Consider the following subspace of R^3:
W={(x,y,z)belong to R^3|2x+2y+z=0, 3x+3y-2z=0,x+y-3z=0}
The dimension of W is
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B2y%2Bz=0
3x%2B3y-2z=0
x%2By-3z=0
Use row operations to show that rows 1 and 3 and rows 2 and 3 lead to z=0.
R%5B1%5D-2R%5B2%5D=0
R%5B2%5D-3R%5B3%5D=0
That leaves you with
x%2By=0
y=-x
So only 1 independent choice of variables.
dim%28W%29=1