# problems3.1 - Math 307: Problems for section 3.1 February...

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Math 307: Problems for section 3.1February 2, 20111.Show that ifPis an orthogonal projection matrix, thenbardblPxbardbl ≤ bardblxbardblfor every x. Use thisinequality to prove the Cauchy–Schwarz inequality|x·y| ≤ bardblxbardblbardblybardbl.2.Use the Cauchy–Schwarz inequality for real vectors to showbardblx+ybardbl2(bardblxbardbl+bardblybardbl)2Under what circumstances is the inequality an equality?3.Using MATLAB/Octave or otherwise, compute the matrixPfor the projection ontothe line spanned by a=1201inR4.Compute the matrixQfor the projection onto the(hyper-)plane orthogonal to a. (Provide the commands used.)4.Using MATLAB/Octave or otherwise, compute the matrixPfor the projection onto theplane spanned by1110,0123and1013. (Careful: these vectors are not linearly independentsoATA

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Term
Fall
Professor
RICHARDFROESE
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