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MissTica
3 years ago
14

Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, where

Mathematics
1 answer:
Gwar [14]3 years ago
7 0
To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors. 

<span>Define projection of v on u as </span>
<span>p(u,v)=u*(u.v)/(u.u) </span>
<span>we need to proceed and determine u1...u5 as: </span>
<span>u1=w1 </span>
<span>u2=w2-p(u1,w2) </span>
<span>u3=w3-p(u1,w3)-p(u2,w3) </span>
<span>u4=w4-p(u1,w4)-p(u2,w4)-p(u3,w4) </span>
<span>u5=w5-p(u4,w5)-p(u2,w5)-p(u3,w5)-p(u4,w5) </span>

<span>so that u1...u5 will be the new basis of an orthogonal set of inner space. </span>

<span>However, the given set of vectors is not independent, since </span>
<span>w1+w2=w3, </span>
<span>therefore an orthogonal basis cannot be found. </span>
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