Let W be the subspace spanned by the given vectors. Find a basis for

generals336 2021-09-27 Answered

Let W be the subspace spanned by the given vectors. Find a basis for
w1=[1132],w2=[0121]

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Expert Answer

broliY
Answered 2021-09-28 Author has 97 answers

Let
A=[w1 w2]=[10113221]
We know that W=(col(A))=nul(AT) so let's we find null space of AT
We see that
y=[y1y2y3y4] W
if y1+y3y4=0 and y22y3+y4=0. Then
W={[y3+y42y3y4y3y4]}={y3[1210]+y4[1101]}=([1210],[1101])
Result:
W={[y3+y42y3y4y3y4]}={y3[1210]+y4[1101]}=([1210],[1101])

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