Science:Math Exam Resources/Courses/MATH221/April 2010/Question 09
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Question 09 |
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Let W be the subspace of spanned by and . Find the vector in W which is closest to . |
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! |
Hint |
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Science:Math Exam Resources/Courses/MATH221/April 2010/Question 09/Hint 1 |
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Solution |
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We can make a matrix out of the vectors that span W therefore the columns of A are linearly independent and we can compute the projection matrix P using the equation
The vector in W closest to the vector v can be found by taking the projection of |