Name:Thursday section time:Student ID:Math 20F - Linear Algebra - Spring 2003Answers to Self-assessment Quiz #5.5 — May 22You must show your work in order to get credit for a problem.Label your answers clearly.1.Letu1= (1,1,1,0)Tandu2= (0,1,1,1)T.LetU=Span(u1,u2).Find a basis forU⊥.ANSWER: Form the matrixA=11100111¶. The nullspace of thematrix is equal toU⊥, sinceR(AT) =U. After finding also solutionstoAx=0(details of work omitted), we haveU⊥=Span((1,-1,0,1)T,(0,1,-1,0)T).2Find the linear function that best approximates datax-2012y2012in the least squares sense.
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