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MATH 330 Final Exam Outline

# MATH 330 Final Exam Outline - Math 330 Final Exam Outline...

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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 9:45-11:45 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 re-takes 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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MATH 330 Final Exam Outline - Math 330 Final Exam Outline...

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