Hello,
(1)
(2)
(3)
(4)
(2)+(3) :
So the system is resumed to :
(1)
(3)
(4')
(1')
Now, keep the value for x_4=0.
Then replace x_5 by 0 for example and for 1. Then you will have x_3 thanks to (4')
And for x_1+x_2 do the same !
Find a basis for each of the subspaces.
1. The subspace R^5 given by the solution space of the homogeneous system system
2x_1+2x_2-x_3+x_5=0
-x_1-x_2+2x_3-3x_4+x_5=0
x_1+x_2-2x_3-x_5=0
x_3+x_4+x_5=0.
2. The subspace of R^6 given by
W={(u,v,w,x,y,z) in R^6: u+w=v-x, v=y+z}