How to show that a set of vectors is a basis for U ? 
QUESTION
- Let U ={(x,y,z,w) \in R^4 | x= y+z+w and x+y = z+w}.
- show that s = {col {1,0,1,0}, col {3,0,1,2} }is a basis for U.
2026-04-12 11:36:12.1775993772
How to show that a set of vectors is a basis for U where U is a set of columns?
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You have to show:
The defining equations for $U$ are linearly independent, so that $U$ has dimension $2$.
The vectors in $S$ are linearly independent and belong to $U$.