5. Let u be a unit vector in R”. Let A = In – uu?. a)....

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5. Let u be a unit vector in R”. Let A = In – uu?. a). Verify that A is symmetric, that is, AT = A. b) Verify that A is idemp

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soth G het ube a unit rector in 12h set A = In – uut. : AT=(In - u ut) @ = IXT - Uut) = In - (UT) ut = In- uut [rut=u] 1. A Also, since 2= re. u U and vou is a - 11u112 sealas, z is a vector parallel to u. Hence from . w=w+z. The problem follows. c)

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