Question

Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference instead of a sum. OD. Rewrite p+ S as a product instead of a sum. How would p+S be rewritten? OA. p S is the set of all vectors of the formS+S. OB. p+S is the set of all vectors of the form cp, where c is a scalar. O C. p+S is the set of all vectors equivalent to p-S. OD. p+s is the set of all vectors of the form p+v, where v is a vector in S. T is defined as a transformation from Rm to Rn. Which of the following transformation rules will be used here? T(cx-cT(x) for all scalars c and all vectors x in Rm. O B. T(u-v)- Tv)-T(u) for all vectors u, v in Rm. A. t(스)-T(x) for all scalars c and all vectors x in Rm O D. T(u+v)-T(u)+T(v) for all vectors u, v in Rm State how this can be used to prove that the image of p S under T is the translated set T(p)+T(S) in R" O A. Applying T to a typical vector in p S, we have T(cp cv) cT(p)-cT(v), where c is a scalar and v is a vector in S. This vector is in the set denoted by T(p)+T(S) because v is a vector in S and the scalar is OB. Applying T to a typical vector in p S, we have T(cp+ S)-cT(p)+S, where c is a scalar. This vector is in the set denoted by T(P)+T(S) because p is a vector in S. O C. Applying T to a typical vector in p+ S, we have T(S+S) T(S)+T(S). This vector is in the set denoted by T(p)+ T(S) because p is a vector in S. D. Applying T to a typical vector in p+s, we have T(p)-TIp)+Tv), where v is a vector in S. This vector is in the set denoted by Tip)+T(s) T(p)+T(S)

Answer 1

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