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## Homework Statement

We are given the following subspaces

U := {x E R3: x1 + 2*x2 - x3 = 0}

and

V := {x E R3: x1 - 2*x2 - 2*x3 = 0}

And we need to find a basis for

(i) U

(ii) V

(iii) U n V (not an "n" but a symbol that looks like an upside-down U)

(iv) span(U u V) (not a "u" but a symbol that looks like a U)

**2. The attempt at a solution**

Because x is a subspace of R3 in both V and U, it seemed that for (i) and (ii) the trivial basis would simply be e1 = [1,0,0] e2 = [0,1,0] and e3 [0,0,1]

I also do not know what the U and upside-down U symbols mean, but someone guessed that "n" meant where they overlap and "u" meant the combination of both subspaces

The answers I found seem to trivial, am I missing something very obvious, and could anyone give me any suggestions to lead me in the right direction

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