# 8.5WebPage - YIYAO LIU Math 308, section E, Fall 2014...

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Current Score :– / 22Due :Friday, December 5 2014 10:00 PM PST1.–/2 pointsHoltLinAlg1 8.5.001.Find the vector in the subspaceSclosest toy[-7/2; 7/2]811.isUW Common Math 308 Section 8.5 (Homework)YIYAO LIUMath 308, section E, Fall 2014Instructor: Richard BalkaWebAssignThe due date for this assignment is past.Your work can be viewed below, but no changes can be made.Important!Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor maynotgrant you anextension if you have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key.Request Extensiony=,S= span1..
2.–/3 pointsHoltLinAlg1 8.5.003.Find the vector in the subspaceSclosest toy.[20/21; -37/21; 52/21]Solution or ExplanationAn orthonormal basis forSis given byandThe vector inSclosest toyisy=,S= span,113123511v1=/=12312311414171431414v2=/=.511511593193193projsy= (v1·y)v1+ (v2·y)v2=·+·=.1141417143141411311414171431414593193193113593193193202137215221
3.–/2 pointsHoltLinAlg1 8.5.005.Find the normal equations for the given system.[69; -1]The normal equations,are thus given by3x1x2=x1+3x2=5x1x2==355511x1x2or858=..,.

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