i am given these 2 groups(adsbygoogle = window.adsbygoogle || []).push({});

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

-----------------------------------------------

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

------------------------------------------------

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

------------------------------------------------

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Subspaces and basis

**Physics Forums | Science Articles, Homework Help, Discussion**