# Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra4th QuizApril 8, 2005Problem 1Let~ei,i= 1,2,3,4 be the standard basis ofR4.Is there anorthogonal matrixAwithA~e1=120012, A~e2=1200-12, A~e3=0100, A~e4=0020or not? If so, findA, and if not, explain.Problem 2Find an orthonormal basis for the subspaceVR3spanned bythe vectors101,110.Moreover, find a normal basis for the orthogonal complement ofV.Problem 3Let{1, ~α2, . . . , ~αk}be a set of mutually orthogonal vectors in