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$4.00 Orthonormal Vs. Orthogonal....

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TAboy26
TAboy26
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Q:
see attached JPG file..
Correction..in A its find the Orthonormal basis instead of Orthogonal!!!!!!
many Thanks!!
 
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  • Posted on Feb 06, 2009 at 10:28:28PM
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alephzero314
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A:
Preview: ... <br><br>w1 = (12,-3,0)<br>w2 = (0,1,-12) - (0,1,-12).(12,-3,0)/(144+9) * (12,-3,0)<br> = (0,1,-12) - (-3)/153*(12,-3,0)<br> = (0,1,-12) + 3/153 (12,-3,0)<br> = (0,1,-12) + (36/153, -9/153, 0)<br> = (36/153, 144/153, -12)<br><br>So the set {w1,w2} is an orthogonal basis for the desired subspace.<br><br>To get an orthonormal basis, we have to normalize.<br>Let x1 = w1/|w1| = (12,-3,0)/sqrt(153) = (12/sqrt(153),-3/sqr ...
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