A 2 Let T R R Be A Linear Transformation And Ver Be A Nonzero Vector We Denote By Ky Be The Smallest Natural Numb 1 (25.2 KiB) Viewed 20 times
A 2 Let T R R Be A Linear Transformation And Ver Be A Nonzero Vector We Denote By Ky Be The Smallest Natural Numb 2 (25.2 KiB) Viewed 20 times
a 2. Let T:R" →R" be a linear transformation, and veR" be a nonzero vector. We denote by ky be the smallest natural number such that v, T(v),T?(v).....Tk (v) is linearly dependent. (Note that Tº =TOT, T* =TOTT, etc. Also note that T"(v) just means v.) (a) Let Srv := spanív, T(v).....Tky--(v)). Prove that Stv is 1-dimensional v is an eigenvector of Ar. (b) We say v ER" is cyclic if Srv = R". Let T: R3 R3 be given by r T 2+y (x + y + ] Prove that y is cyclic +0.
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