- #1

Dell

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- 0

^{1..4}in vector space W

W=sp{(X

_{1},X

_{2},X

_{3}X

_{4})[tex]\in[/tex]r

^{4}| X

_{1}+2X

_{3}+X

_{4}=0}

Find the basis of W,

what i did was--

for these to be the basis of W they need to span W and be independant of one another,-

since X

_{1}+2X

_{3}+X

_{4}=0 it is clear that these 3 are not independant, since X

_{1}+2X

_{3}=-X

_{4}etc..

does this mean that dimW=3 and i can take any combination of 3 of the 4 x's for my basis as long as X

_{2}is one of them?