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Unformatted text preview: Math 330  Final Exam Outline The final exam for math 330 will take place Friday May 8 from 9:4511:45 AM in our usual classroom WRB 2024. A calculator for arithmetic is allowed but nothing that has any matrix or symbolic capabilities is permitted. It should be obvious but please note There are no retakes on the final. Basic Dot Products 5 points Given two column vectors vectorv and vectorw you will be asked for the following: vectorv vectorw  vectorv  (Be sure to simplify any radicals). The distance between vectorv and vectorw . Basic Projections 5 points You will be given a column vector vectorv in R n along with an orthogonal basis { vectorw 1 , vectorw 2 ,..., vectorw p } for a subspace W of R n . You must then project vectorv onto vectorv W . This is simply vectorv = p summationdisplay i =1 bracketleftBigg vectorv vectorw i  vectorw i  2 bracketrightBigg vectorw i QR decomposition 10 points You will be given a matrix A from which you must find a factorization of the form A = QR where Q has orthonormal columns and R is upper triangular. This is accomplished by applying the Gram Schmidt algorithm on the columns of A from left to right, and then normalizing all the vectors when you are done. Once you have Q it follows that R = Q T A . Note that it could happen that the columns of A are dependent. This will lead to a situation where one of the potential column vectors of Q is zero and we omit it....
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 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra, Dot Products, free variables, Rm Rn

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