MATH221 December 2008
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Question 04 (b)
Let W be the plane in spanned by the vectors and . Find the vector in W which is closest to .
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Think about orthogonal projections. Part (a) could be helpful.
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The vector in W which is closest to b will be the orthogonal projection of b onto W . From part (a), we know that the vectors and form an orthogonal basis for W. Let us make an orthonormal basis by normalizing u and w to
Then the orthogonal projection of b onto W is
Thus is the vector in W closest to the vector
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