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3. Are the following functions below linear? If they are, give the associated matrix. If the function T is not linear, prove it by doing
3. Are the following functions below linear? If they are, give the associated matrix. If the function T is not linear, prove it by doing exactly one of the following: . Find vectors 7 and w in the domain such that T(7 + w) # T() + T(w). . Find a vector 7 in the domain of the functions and a scalar o in R such that T(av) # aT (U). (a) (/10) The function 7 : R - R' given by the formula T(x) = T2 (b) (/10) The function 7 : R' -> R defined by the formula T( ) = 13 + CA(c) (/10) The function 7 : R* -> R defined by the formula T( (d) (/10) The function T' : R3 - R' which takes a vector v to its reflection across the line ! = I. (e) (/10) The function / : R' - R' defined by the formula I( =
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