- #1

Dell

- 590

- 0

W=sp{(1 0 2 0) (1 1 1 1) (1 0 0 0)}

U=sp{(1 0 1 1) (1 2 1 2) (0 0 1 0)}

and am asked to find

a basis for each one and their dimention

a basis for W+U

a basis for W[tex]\cap[/tex]U

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for the basis i found that they are both linearly independant therefore my basis is the span given and the dimention is 3 for both of them

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how do i find a basis for W+U? can i take the 6 vectors given and check which are dependant and which are independant, take the independant ones in which case i get

w+u=sp{(1 0 2 0) (1 1 1 1) (1 0 0 0) (1 0 1 1)}

dim(W+U)=4

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for W[tex]\cap[/tex]U am i looking for all the vectors in W which are perpendicular to U? how would i do this?

i know how to find one vector perpendicular to a subspace but how do i find a basis for a group perpendicular to another group