- #1
fishingspree2
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We have W = [v1,v2,v3,v4]
v1=i-k
v2=i+j+k
v3=j+2k
v4=2i+j
Show that W is a subspace of V3.
first, vector 0 is obviously in W.
then,
let u = n1v1+n2v2+n3v3+n4v4 ∈ W
and v = s1v1+s2v2+s3v3+s4v4 ∈ W
and p ∈ reals
then u+pv
=(n1+ps1)v1+(n2+ps2)v2+(n3+ps3)v3+(n4+ps4)v4
∈ W
Am i completely proving that W is a subspace of V3 (the 3 dimensional space)? I am not quite sure because I am not even using the explicit given vectors.
Thank you very much
v1=i-k
v2=i+j+k
v3=j+2k
v4=2i+j
Show that W is a subspace of V3.
first, vector 0 is obviously in W.
then,
let u = n1v1+n2v2+n3v3+n4v4 ∈ W
and v = s1v1+s2v2+s3v3+s4v4 ∈ W
and p ∈ reals
then u+pv
=(n1+ps1)v1+(n2+ps2)v2+(n3+ps3)v3+(n4+ps4)v4
∈ W
Am i completely proving that W is a subspace of V3 (the 3 dimensional space)? I am not quite sure because I am not even using the explicit given vectors.
Thank you very much