in linear algebra, if i am told to find a basis for the following(adsbygoogle = window.adsbygoogle || []).push({});

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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# Finding the basis of this subspace

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