- #1
Dell
- 590
- 0
in linear algebra, if i am told to find a basis for the following
W={(x,y,z,t)|x+y=0, x+t=0}
what i did was
1 1
1 0
0 0
0 1
after performing elementary actions on rows, i came to
1 0
0 1
0 0
0 0
from here i can see that they are linearly independant and they cleary span their own space so they are my basis.
basis= (1,1,0,0) (0,1,0,1)
the correct solution in my book was quite different, they put the vectors lying down like so
1 1 0 0
0 1 0 1
and eventually got to
1 0 0 -1
0 1 0 1
what is the reason that my way is wrong,
W={(x,y,z,t)|x+y=0, x+t=0}
what i did was
1 1
1 0
0 0
0 1
after performing elementary actions on rows, i came to
1 0
0 1
0 0
0 0
from here i can see that they are linearly independant and they cleary span their own space so they are my basis.
basis= (1,1,0,0) (0,1,0,1)
the correct solution in my book was quite different, they put the vectors lying down like so
1 1 0 0
0 1 0 1
and eventually got to
1 0 0 -1
0 1 0 1
what is the reason that my way is wrong,
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